When would I use “kshe” vs “matai” ?

See a translation

מתי (matai) is a question word meaning When. So when you're interested in When something is going to happen or When did it happen, you use מתי.
מתי הוא חוזר? - when does he come back?
מתי הוא חזר? - when did he come back?

כש- is basically the word כאשר only used as a prefix for the following word. It also means When, but not in a questionable manner, but for a statement of a moment or a time when something happened or will happen.
כשהוא חזר, הייתי כבר במיטה - When he came back, I was already in bed.
כואב לי הראש כשאני מתעורר - My head hurts when I wake up.

- מתי נבקר באמריקה? - When will we visit America?
- כשחזירים יתחילו לעוף - When pigs will start flying.

But sometimes you can use מתי this way:
- מתי אתה רוצה לבוא? - When do you want to come?
- מתי שנוח לך - When it's comfortable for you.
But here we use מתי ש-, to make it similar to the כש- usage.