Giving an address on an Ethereum rollup
Wallets show one 0x… address for Ethereum, Base, Arbitrum, Optimism and Polygon. The payout here is on Ethereum itself. If you expect the USDC on Base and give the same address, the tokens will be on Ethereum at that address — recoverable, since you hold the key, but not where you wanted them and only movable with ETH for gas.