Can air be trapped on the wet side of an expansion tank's diaphragm?
Water heater expansion tanks come in various sizes. 2.1 gallon, 4.5 gallon, etc. The minimum size depends on your water pressure and the size of your water heater. You can do a calculation or use the vendor's sizing table. A water heater expansion tank bigger than the minimum is not a problem at all. A bigger water heater expansion tank is actually better in the sense that for a given water heater size, the pressure rise is lower.

What does it mean to have air trapped on the water side of the diaphragm? It means your expansion tank acts like a bigger one, until that trapped air dissolves. So you have nothing to worry about.