If my tax returned was e-filed, does that mean I have to physically print out the copies and then mail it ?

No.  If you e-filed you do not have to mail anything.  But it is a good idea to print out a copy for your own records.  

https://ttlc.intuit.com/community/prior-year-return/help/how-do-i-get-a-copy-of-a-return-i-filed-this-year-in-turbotax-online/00/25932

No.  When you efile you don't need to mail anything.  That's one of the benefits of Efiling.

Did you go all the way through the File tab, through the 3 steps and hit the big orange Transmit Returns Now button?

You can check your efile status here     

https://turbotax.intuit.com/tax-tools/efile-status-lookup/   

To check in the Desktop program open your return and go up to menu item

File > Electronic Filing > Check Electronic Filing Status

When you efile you get back 2 emails.  The first email only confirms the transmission.  The second email says if the IRS (or state) Accepted or Rejected your efile.

When you log into your account you should also see the status and if it was Accepted or Rejected, Started, Printed, Ready to Mail, etc.  What does it say?