I'm going to ask my partner to tell me when he needs his me time.
Well that is nice of you.  What prompted you to want to do this?
He says he needs some time alone.
It's good that you're being considerate of your partner's need for personal space. It's normal, after all, for people to want some time alone every once in a while.
I feel like he's cheating on me and I'm going to use this to catch him.
That's not showing very much trust towards your partner.  It's not right to violate the trust of your partner by trying to catch them in some act.