It seems the Mega Evolved Pokemon are not getting their Abilities after they change, here is what I did to test if this was right;

I first let Venusaur Mega Evolve and do a Non-Damaging move, then I had the opponent swap out to another pokemon with the ability 'Trace'.

The opponent's pokemon traced my M. Venusaur's 'Overgrow' ability. (Which should have changed to 'Thick Fat' after the Mega Evolution.)

I've tested M. Charzard X/Y and M. Blastoise and they have the same issue too.

Switching the pokemon out of battle, then back into the battle fixes this issue and gives the Mega Pokemon the correct ability.