Salt used in Perkin Reaction
The base, as you pointed out is nearly always the salt of the acid corresponding to the annhydride.

This is because the base which differs in structure will react with the given carbonyl compound and yield some other compound rather that abstracting a proton.

Eg.
Let's say you have tertbutyl salt there instead of what we are having right now.The tert butyl could have directly attacked on the Carbon having the double bonded oxygen as it has a partial positive charge due to polarization.Which will result in to eliminating the other symmetric half of the annhydride and replacing it by tertbutyl.This changed your basic reacting molecule.And hence the
 product you obtained is definitely not the right one. Whereas using the salt of the acid that formed the annhydride will not change the annhydride even if it reacts with the annhydride the way I stated above.

Using the salt of the acid they produced the annhydride does nothing but abstracts the proton or simply regenerate the original carbonyl compound/annhydride if it reacts rather than abstracting a proton.