Z is an English letter, pronounced zei.
Don't worry too much about pronunciation. The teacher's different pronunciation may be a personal language habit.
For example, when we were older, we always pronounced c as "xi", which was similar to the sound of "Xi", which was wrong.
In the past, when physics teachers read G, they always read "Ji" as "chicken", which is also wrong.
For another example, when we used to pronounce "chlorine" as "road", we should actually pronounce it as "green".