Although there has been a bit of retconning going on, play through EW's story, it explains the situation (basically
the Blessing of Light prevents aetherial manipulation like tempering, which is a spell Venat created before she became Hydaelyn.
And incidentally, exactly how much of Hydaelyn really is a Primal and how much is just Venat's natural Ancient transformation ability as an Unsundered is a very good question (think Emet turning into Hades at the end of ShB).
Basically, no, the WoL is not tempered by Hydaelyn. Reincarnated by her endlessly throughout history yes, but not tempered (that was just an old headcanon theory from years ago that never had much weight).