Sasuke's ms has nothing to do with naruto.
Originally Posted by Gaara Kazekage
He awoke his ms after learning about itachi's life. There's no evidence that suggests you don't need to experience the pain of loss in some way at the moment.
The only way to know for sure is to learn how kahashi did it.
To obtain an MS you need to experience the death of a person who is closest to you. You must feel the emotion of losing that someone, and killing them doesn't necessarily activate it.
It has been hinted that Kakashi's other team mate Rin has died. So maybe Kakashi suffered the loss of Rin, and thus awakening his MS?
Well, for all we know about Kakashi it might have happened anytime along the road. Most likely he got it during the time skip Original-Shipuuden. but he can also have awaken it a lot earlier and chose to keep it a secret until he really needed it.
It's like Psukkar say's, we can't know for sure how MS works until we know how Kakashi did it