Multiple Apple IDs on one new iMac

I'm relatively new to the apple world so pease excuse my lack of knowledge. I just bought a Mac and will be syncing an iPhone 5 and an iPhone 5c to it. The two phones share one apple ID for iTunes, but each has a separate apple ID for the iCloud. I'm not sure we should have set up the phones this way, but that's how it was recommended when we bought them. Anyway, my question is this: do I understand correctly that we can only authorize our new computer to recognize one of the apple IDs now, and the other will have to wait 90 days? Thank you.