1- Durring the cinematic I mentioned above, Ganondorf survives his execution because of the power of the Triforce of Power. In the "child timeline" Ganondorf never got the Triforce so how could he use it to save himself. And to those who say that once he got it in the future he got it through all time periods, this is rediculous. If this was true then Link and Zelda would have also had their pieces in the past and OoT would have been a much different game.
It is described in TP that Ganondorf acquired his piece of the Triforce "by some divine prank". So like Zemen said above, he doesn't know how he got it, and really neither does anyone else. The word "divine" usually applies to the work of a god or goddess. So my guess is that the goddesses placed the power of the Triforce into Link, Zelda, and Ganondorf by the time of his execution anyway. It is said throughout one of the games, maybe multiple games, that there are three chosen to hold the Triforce. These three are the different generations of Link, Zelda, and finally, the one and only Ganondorf.
2- Several very distinct references are made throughout TP which point to its placement in the "adult timeline".
First, at the beginning you get the Hero's Clothes which it strongly implies were once worn by the Link in OoT. But if this was the "child timeline", there was Hero of Time. If Ganondorf was executed before he could conquer Hyrule, then the events of OoT never happened and Link was just Link if you catch my meaning. The only one who would have known that Link was anything but a 'forest boy' was Zelda. Furthermore, Link in OoT didn't recieve his Hero's Clothes until he was an adult. So they would never have existed in the "child timeline".
Like some above posts mentioned as well, young Link was a hero in his own right. Zemen mentioned that it did not mention the Hero of Time specifically, on the "hero". However, I believe that the story of the Hero of Time is still known to the people of Hyrule even in the Child Timeline. The intro to Wind Waker tells of the Hero traveling through time to save Hyrule. I would assume that by young Link telling Zelda, who informs the King, of Ganondorf's plans, he had to have mentioned that he went through time to do so. I doubt Link only said "Ganondorf is a bad guy", to Zelda. He probably told her of his entire adventure, which was passed down through legend.
Second, when you recieve the Zora's Tunic in TP Rutela says her husband, King Zora, made them for a great hero. this didn't happen until Link in OoT was an adult. So if this happened in the "child timeline", these could not possibly have been made for the Hero of Time.
That is a good point. But the Zora Tunic appears very different from the one in OoT. Maybe they just wanted to add details to it, who knows. Some people speculate that the King Zora mentioned in TP is a different one from the King Zora in OoT, which is possible. There was a King Zora in OoA as well. But that would cause a problem with the timeline if it were talking about the Hero of Time. One thing though, is that the Zora Tunic in OoT wasn't actually made by King Zora. The tunic already existed. You could even buy one in the shop in Zora's Domain. King Zora simply gave one to Link.
And Third, we see the Biggoron Sword on display in Hyrule castle in TP. This sword was not completed and used by the Hero of Time until he was an adult. Again, this item would not exist in the "child timeline".
Most likely a cameo. If it were the actual Biggoron Sword, and had any symbolic value or relativity to the timeline or the Hero of Time, they would have put a description below it. Besides, there are notable differences in the Biggoron Sword and the one shown in the castle. But I would think that they intended it to be the Biggoron Sword, strictly making a cameo appearance.
Oh and Fourth, the fishing hole in TP has a picture of the master fisherman from OoT holding the Hylian Loach caught by Link, which didn't happen until he was an adult.
Honestly, I can't say that I remember this. I didn't spend a whole lot of time in the fishing place in TP, nor have I ever actually fished in the game. But if it just showed a picture of the fisherman holding the Hylian Loach, with no description, anyone could have caught it. The fisherman himself could have caught it.
The idea that TP comes on the Child Timeline, opposite of WW, is quite obvious to me. There are more things that point to it being where most believe it is than things that may barely cause it to appear on the Adult Timeline. For example, the whole excecution scene would not have taken place had Ganondorf been locked away in the Evil Realm as he was at the end of OoT. This event, taking place on the Adult Timeline, was proven to be consistent until he managed to escape, which caused the events of WW. If TP took place on the AT, then technically, it would have to come before WW, which would then cause WW's backstory and multiple elements connecting it to the AT of OoT, useless. And we know for a fact that WW comes on the Adult Timeline after OoT because of countless references made throughout OoT, such as the main factor of the Hero of Time not returning. He didn't return because he was sent back through time. Link never went back forward through time afterwards, and he sure wasn't stuck in Termina because he left after defeating Majora. The final scene of the game shows Link on Epona back in the Lost Woods.
Another big thing is the Sages. They have no specific features like the ones in the Adult Timeline of OoT do. That is because the Sages did not have to awaken in Saria, Darunia, Ruto, etc., in the Child Timeline, because the Temples throughout Hyrule never became infested with evil. Whenever Ganondorf entered the Sacred Realm and claimed the Triforce, it is said that the realm became a place of evil. I believe this comes from some text in WW. Anyway, the Sages protect the temples, and the temples are linked with the Sacred Realm. The sages had to awaken in those people from OoT because of Ganondorf entering the SR and causing all the evil to get into the temples. That is why the stained glass in Hyrule Castle in WW, where the Master Sword is held, shows the Sages as they were from OoT; because they were awakened as such on the Adult Timeline. Had these Sages not been awakened, they would have kept their original form, which is showin in TP. And of course, in the Child Timeline, they were not awakened, which is why they appear the way they do in TP.
Last, a main selling point is the location of the Master Sword. Before TP, we saw this blade play big roles in OoT and ALttP. In OoT, it was located in the Temple of Time. In ALttP, it was in the Lost Woods for some odd reason. By the time TP comes out, we see the Master Sword in the ruins of the Temple of Time, where the Lost Woods have apparently extended onto. So if you are convinced by geographical changes, this is a key point:
*Master Sword in pedestal in Temple of Time at end of OoT
-Some hundred years later, Lost Woods grow around the Temple of Time, which has fallen apart
**Master Sword in pedestal in Temple of Time ruins, becoming the Lost Woods
-Some hundred years later again, ruins are completely gone. Lost Woods have grown extensively, only the pedestal now remains.
***Master Sword in pedestal in Lost Woods
Also, you say that the developers could easily come back and change their minds about the timeline, making it linear again or possibly putting TP on the Adult Timeline. I have give my reasons why TP can't go on the AT. For the developers to change their minds now about the split would be rediculous. It would cause way too many problems with the games.
This is how the linear timeline supposidly looked prior to the split
OoT/MM--ALttP/LA--LoZ/AoL--OoX or OoT/MM--ALttP/LA--OoX--LoZ/AoL
With the Oracles changing their position, since they are still pretty much up for debate and can go either place. These were the only games before WW, and it is easy enough to make a timeline without WW at this point. After Ganondorf was sealed in the Evil Realm at the end of OoT, Link went back in time to Termina, then that was it for that Link. Later on, Ganondorf, still sealed away, turns the SR into the Dark World. That causes ALttP, followed by LA. Later, Ganon is attempted to be revived by Twinrova in OoX. That doesn't work. Then later he shows up in LoZ somehow. Or just switch those last two sentences around for the second version of the linear timeline.
Now when you throw WW into that mix, then your saying that Ganondorf actually escaped prior to ALttP. The story suddenly begins focusing on what happened after Link went back through time. Ganondorf escaped, and Link was not there. It put an entirely new story in there between OoT and ALttP, which has to be fitted in that position. ALttP now cannot come after WW because Hyrule is gone. That makes the split official. But even if you still weren't swayed by WW, you have TP to come out, and clearly shows what happens after the events of the Child Timeline, which even further solidifies the idea of the split timeline. You have TP, a game that fits easily between OoT and ALttP on the Child Timeline because of various reasons mentioned above.