How the first succesful miner is ensured his reward
By definition, by altering the block, the hash would have to be altered too. Thus the hash ensures the block can't be tampered with, and the miner safely receives his reward.

To modify the block, the attacker would have to recompute a new valid hash within the difficulty, i.e. mine the block again after the original miner, which would clearly not be part of the main chain by that point and thus basically ignored.