It sounds like you need to set up Exchange Hybrid although it's really not clear to me what you're actually doing.

What is the "secondary server?" How did all this work before you bought "MS accounts?" Where was the MX pointing before? When you say "Exchange server" are you talking about Exchange Online or onprem? Which server is rejecting with the relay error?

Regardless, you're going to need objects in the environment where the MX points that forward to the second location where the rest of the users are. In Exchange onprem/Online this would ideally be a MailUser object created by Azure AD Connect, but a Contact could suffice in certain setups.

And the second environment needs to trust the emails forwarding through the first or you'll have SPF failures.

But again, a proper Exchange Hybrid setup takes care of all of this.