As far as I know there's nothing you can do to change the behavior in Find/Change.
Ah, the old history: Adobe's staff do not use ID. Just Word.
BUT, it is something I can do: just purchase a dedicated script/plug-in and kindly send the invoice to Adobe, to be discounted from my monthly invoice.
In this second example the thing is really delirious. After the change is made ID jumps to an absurd place of the page. Cannot believe it. Many years suffering this!
No more ipse lorum. Better:
Quo usque tandem abutere, Adobe, patientia nostra
Yes, the spelling check exhibits a similarly annoying behavior. To some extent, I've learned to live with it by advance-managing the view somewhat. Note while these routines move (pan) the view around as items are found, the zoom level does not change, so depending upon the proportions of your project, it may be advantageous to start either zoomed out or zoomed in. Generally speaking I like it zoomed in for spell check because it helps offer a fast view of the offending word; but zoomed out works better for Find/Change because more of the spread stays in view so context is more easily perceived.
Zooming out helps a little but here it gets smaller than required.
I will post in the script section.
If possible, may be between a dozen of ID slaves (you and me are two, now) and we may pay a script and sent to Adobe with the next upgrade.
There is, actually, a fantastically convenient plugin on the Adobe Exchange (Window>Extensions>Adobe Exchange) called "Always Fit Spread", by Bookraft Solutions*, which adds a menu item to the View menu: "Always Fit Spread in Window".
Click on this menu item to force InDesign to show the entire spread whenever the selection changes (as when you're spell checking, or finding/changing).
I use it daily and couldn't manage without it!
*Disclosure: That's me
PS There's a trial version
PPS If you have any trouble with it, please email me at admin (at) freelancebookdesign.com
It is the heaven, Ariel.