“Search and Replace” not really searching and replacing?

I’m having an issue that others appear to have griped about, but I’ve yet to find an answer. Whenever I use the search and replace feature, it makes the changes on the live site, but not on the backend. For instance, if I replace https://www.firstsite.com with https://www.secondsite.com, the back end will still say “www.firstsite.com” in the post draft, but if I preview or publish that draft, it will read “www.secondsite.com” in the live version.

I’m worried about the implications of this. Does this mean that if I migrate my site or make any updates (such as delete the search and replace plugin) that my changes will be completely void?