That's not a bad start. It's important when apologizing not to deflect the blame. So don't say things like "I'm sorry you made me do this." or "I'm sorry but you did this first". This makes the apology feel insincere, making it seem like the blame is being pushed to the other person.

[She's almost slightly impressed, that Jinx is starting strong? But she's not convinced this is going to continue to go well.]

So, you could continue that with something like "when you and Vi killed each other, it made me feel..." and be honest with him, about how you felt. He won't know how much he hurt you, unless you tell him.