This is one of my favourite "bugs".
For various reasons (which I honestly don't understand) there isn't enough logic behind the Vichy decision. IMHO that is.
Even as Japan, if you conquer all of Cambodia & Vietnam, it gets given to Vichy when France falls. Whereas, if Japan leaves it alone, it all gets given to Japan.
All I do is just re-conquer. The troops stationed there are even more of a push-over but... this depends upon you being allowed the DoW.
Conquered by an Axis Siam though... It is possible (even probable) that Germany would have required Siam to give them up to Vichy if Japan wasn't in Axis (which she shouldn't be until after The Fall of France) but the greater chance is that Japan would have simply demanded them from Siam in order to "protect" them from the Europeans. That would have meant war between Japan & Siam regardless of Siam’s Axis membership. Japan had no fear of Germany and could, quite conceivably, have relished the idea of being on the side that would put positive political pressure on the USA in her favour, to say nothing of removing Allied support from China.
What to do? Re-conquer if you're allowed the DoW. Otherwise, accept an "unfair" political situation where the greater bias of your German "masters" is in favour of your former enemy.