They add to everything. If you have strike tiles with X damage (total) on them then they add to match damage, to ability damage, and even to attack tile damage (M Storm, Doom, Punisher).
They only add once to each -- so match3 becomes match3+X; match4 becomes match4+X, attack tiles become (sum of all attack tiles) + X. Otherwise a single strike tile plus Modern Storm would be... ugly.
The damage is now reduced in cascades -- it's (base + strike) * reduction factor; this is a fairly recent change. It used to be (base * reduction) + strike -- which was really, really nasty and potentially overpowered.