When a general have an ability called “Extra Strike”, they will get an extra attack/action when a specific tile type is matched. For example, C/A Extra Strike ability allows a general to get an extra attack/action whenever Cavalry/Archer tiles are matched, eventhough the general’s troop category does not belong to that particular troop type. Note that Extra Strike will stack with any Normal Attack or Normal Action. A general can have at most 2 Extra Strikes in a single turn. Any excess Extra Strikes acquired by the general that turn will be not be considered.
It is very possible that you matched more than a single type of tiles and as a result two or more troops category can attack on this turn and/or get an Extra Strike. This is where your decision matters. Your skill in match 3 will play a big role in your success in battle.