I filed my federal tax via e file....do I have to also mail the return to the IRS as well?

No, that's part of the beauty of e-filing... there's nothing more to do once you have filed (unless your filing instructions specifically ask you to mail something in... unusual).

If that is the case, why does the program tell us we have to?

Not all returns can be efiled.  What does it say you need to mail?  Maybe a 1040V payment voucher with a check? 

Did you try to efile?  You can check your efile status here https://turbotax.intuit.com/tax-tools/efile-status-lookup/