Keeping an icon of Turbotax in the dock should have nothing to do with it's ability to update. The dock is just an alias of the program. (You do need to have the CD ejected, or if you used a downloaded installer, you have to eject the virtual disk image window. The CD and disk image are read-only and can't be updated.)
I did have the same problem where state forms were not being updated. There is an easy way on the Mac to delete the state formset, then when the program starts up it force-downloads the updated forms.
Go to ~/Library/Application Support/TurboTax Deluxe 2016/Forms and delete the folder for the state formset that needs to be updated.
