Mardu Warshrieker's raid ability isn't a mana ability even though it adds mana. It uses the stack and can be responded to.

Raid abilities care only that you attacked with a creature. It doesn't matter how many creatures you attacked with or which player, planeswalker, or battle those creatures attacked.

Raid abilities evaluate the entire turn to see if you attacked with a creature. That creature doesn't have to still be on the battlefield. Similarly, the player, planeswalker, or battle it attacked doesn't have to still be in the game or on the battlefield.