I just flew JAX-LAS a few weeks ago. Checked both my bag and my wife's bag under my name and we received baggage tags on both.

Flew LAS-JAX back home and checked one bag under my name and the other under my wife's name. My bag had a tag, hers did not.

YMMV, but going forward if we are only checking 2 bags total, I'm going to check both bags in my name and 0 under my wife's name. It seems silly that they would not apply tags to luggage associated with the same PNR. She had the right to check her first 2 bags free, just like a Medallion member, at check-in just without priority tags.

At both LAS and JAX, tagged baggage came out first.