Don't think too hard about the Chronolites, for it will mess up your brain. (I read on TVTropes that "Chronolites" are what they're being called in the French and Spanish translations... such a cool name for them).
In fact, I've learned that any story involving Time Travel will make my brain hurt. The only one that comes close to not giving me headaches is Futurama because they really do have good explaintions for stability when they play with Time. Then, again, the writers on that show are mostly math and science geeks.
I always figured that the Timeshift Stones worked as they do in the present - a stable gateway between *this time* and *this other time* - that is, when the past robots messed with them, they got a glimpse into a bleak, sand-covered future. However, being robots, they probably didn't care too much. A few of them seem to emote a little (like the Skipper), but for the most part, they were just working a job. The "Ooh, the future!" didn't have quite the same "Ooh!" for them as it would for a mortal, perhaps.
Or, perhaps they worked a little differently - subtle timeshifts within the general era that were good for work and whatever the Thunder Dragon wanted to do. Five minutes here, ten minutes there... and they only became the huge time-gap things that they did after a milleinum or two.