Acording to the datasheet the TDA7294 uses -V~s~ and +V~s~ in the block diagram so i would assume it is intended to be used with DC power. If the module is specced for use with AC as well as DC, then this just means what you already suspected: it has an integrated bridge rectifier and most likely some sort of low pass for the rectified power (read: a bunch of big capacitors).

You could just go with a big transformer core that powers them all at the same time; many commercial amps do that and it works fine in general, provided you have enough margin for power spikes and the modules will not influence each other when connected in parallel to power.

In my opinion using separate transformers would be paranoid but it would work of course.

Edit: dont forget that this thing will produce heat. If you really go with an 800W transformer then you have to be able to cool about 400W in the worst case (going by the data sheet power dissipation of the chip and assumed transformer + rectifier efficiency of 90%).