The screen will zoom in automatically when I write.

Is there a way to keep the screen fixed without zooming in?

No, we can't. 

When using the 'Whiteboard' on an iPad, the screen automatically expands when I write letters.
It shouldn't happen. I just try zoom whiteboard on my iPad,  the screen won't be automatically expanded. Could you have accidentally triggered two-finger zoom in/out?  (example : both a finger and hand touched the screen)