Hi Tony,
Yes, the stabilisation mode automatically decides how much zoom is needed to effectively stabilise a video frame (even if you set the Expand to "0").
However sometimes (rarely) small black bars may appear on the edges in case of strong shaking in a frame. In this case, the Expand option will help to correct a frame.
Also if even the "Strong" stabilisation mode doesn't help to stabilise a video frame (or if you want a perfect stabilisation!), the Expand option gives the stabilisation algorithm more screen space for more effective stabilisation. Try values between 5-10 for the Expand option.
Consider another mode - Camera Lock, if the movement in the frame is small (shooting handheld, but the operator tries not to move a camera, not to turn a camera). In this case, stabilisation will be ideal, as if you were shooting from a fixed tripod.
I've checked many video files from different sources, from different cameras. Normal or Strong modes do a good job for 95% of shaky video files without using the Expand option.
In the following promo video, I've used Strong mode for a stabilisation of the 1st video (Expand = "0", by default) and Camera Lock mode for the second video:
https://www.youtube.com/watch?v=oWu-IlXTDvE
P.S. Jill, thanks for your comment!