Memory card question, help needed!

This is probably a stupid question but both me and my son have our own 360 with HDD. I have copied his gamertag to a memory unit so he doesnt have to recover his tag when he plays on my console. My question is does all game progress also store under his gamertag profile on the memory unit? Example, if he plays a game on my console and gets to a checkpoint, will he continue from that checkpoint when he puts his memory card into his own 360?

Would I need to do this everytime he uses the memory card on a different console?

Would I need to do this everytime he uses the memory card on a different console?