Hmmm...so what address are you referring to? The miner's bitcoin wallet address?
By the way, is my revised diagram correct now?
I want to understand how mining works so I'm starting from the beginning - that is, mining on my own first.
Kinda find the diagram for mining pools really complicated - so I'm starting with this first...
your initial diagram sounds like you are saying that the miner first finds the block and then claims the reward which is exactly the opposite of what's happening.
the miner first claims the reward in its coinbase transaction (sends the reward to its own address(es)) then starts mining that block. if they succeed the block will become part of the blockchain and they can spend it later.