Is the Terror "Lifesteal" incorrect on Zane?

While SNTNL is active, SNTNL gains 100% lifesteal while you are affected by Terror

Why is SNTNL getting lifesteal? and not ME!

You don’t technically get the buff either… It’s always the weapon (or melee) that does. It still affects your character fine just one of those wonky translation deals.

The guns on STNL proc life steal for you