The "not our problem, must be Tamron" added a bit of light to the issue. Nikon has not historically supported other manufacturer's lenses so their response is not surprising. Depending on how old your lenses are, Tamron may have firmware upgrades that make the lens more compatible with the newer Nikon bodies.
Your best bet is to check with Tamron on the D600 compatibility issue. You may have to send the lens(s) in for firmware upgrades, etc.
"Red is gray and yellow white, but we decide which is right ....and which is an illusion"