Currently, when executing a series of finds, a document with spreads will jump around within a window, even if view is set to "fit spread in window," as described in this post:

https://community.adobe.com/t5/indesign/searching-a-file-in-indesign-causes-the-spread-to-jump-all-over-the-place/m-p/11118210?page=1#M185629

The expected behavior is that the page where the text is found should be centered on the page. That does not work with spreads. If panels are open on the side of the window, found text can frequently be hidden from view.

So I believe there is a bug with the expected behavior. But it would be even better than the expected behavior if there were a way to make the "fit spread in window" view setting "stick" throughout operations like this, so that both pages of a spread stay in a static position and the cursor merely jumps around.