maybe it was 13th lord commader who was tied to that tree, after it was discovered he had this illicit affair, and, while "awaiting sentencing/punishment" by the nights watch, along comes the CotF with other uses in mind for him.
or
maybe he has the affair AFTER the CotF do their thing...
Nah because Night's Watch was created AFTER the the first White Walkers.
It's pretty obvious, to me, that the book plot is:
1. CotF create White Walkers
2. Last Hero (time traveling Bran?) convinces CotF that this was a big mistake, and they help defeat them.
3. White Walkers create The Wall in their retreat after getting defeated. And/or it's possible that the CotF raised it after making enough headway against them.
4. Night's Watch created, at some point Night's King finds a female White Walker and through the whole sexy time thing gets turned into one himself. Follows the whole tactile conversion thing we've seen in the soul, and the established legend of the dude.
5. Night's King loses, his White Walker woman gets killed, and he's spent the next huge chunk of years regathering strength north of the wall (and watching the Night's Watch dwindle in power and the CotF die off).
6. After creating enough White Walkers from Craster's babies and getting enough wights/skeles it's time to make a move. Also possible (depending on what kind of greenseer abilities he has) that he knows the other moving pieces around the world and that plays some factor in him making a move now.