I'm wondering that myself because I'm a stamina Nightblade and ambush, surprise attack and death stroke all say magicka damage. I wish ZOS will give us some clarification about this.
Ambush, Surprise Attack both scale off stamina and use weapon power and weapon crit. They do physical damage as well as far as I know and use physical resistance and armor penetration. I think it's probably a tool tip error but I could be wrong. I play a magicka nb myself.
On PS4 both Ambush and Surprise Attack are tooltipped as Physical damage, and increase with points spent in Mighty. However the Major Fracture error is there, because it will apply outside of stealth.
Only some nightblade abilities will scale off stamina/weapon dmg and be considered physical attacks when you morph them. Ambush, surprise attack and Killer's Blade are some I am aware of.
I play a stamina nightblade and use those three in addition to dual-wield abilities. I have some magicka-based abilities to dump my magicka like blur and cloak where scaling off magicka is not necessary because they give you a set % buff to dodge and invisibility.