Marking an order received is your signature on the multisig release. It is one of the two signatures needed to move coin out of escrow. The vendor's signature is the other.
What to do first
Physical package in your hands. Opened. Item checked against the listing. Everything matches. Only then mark received.
What not to do
Do not mark received before the package arrives, even if the vendor asks. That is finalising early (FE), and it drops your escrow protection. If the vendor asks you to FE, that is a sign the vendor may not deliver, and you should read the FE-warning reading before responding.
If the item does not match the listing
Do not mark received. Open a dispute with clear evidence. Photos of the package on arrival, photos of the item next to a scale or measuring stick if the issue is weight or size, message log with the vendor showing your polite factual complaint.
What happens after you mark received
Your signature is applied to the multisig release transaction. The vendor's signature is applied automatically or on their next login. When both signatures are present, the transaction broadcasts to the Bitcoin (or Monero) network and the coin moves from the multisig address to the vendor's wallet.
The platform key never moves in this path. That is the healthy signature flow.
Timing
You can wait a day or two to mark received if you want to check the item over. There is no rush. Vendors generally do not follow up until well past the delivery window.