That's one challenge I haven't seen editors tackle correctly by, e.g. having some special condensed view where only lined with cursors are shown so you can see more cursors on the screen and easier scroll around to see even more skipping the rest of the text (like some git diff tools do, showing only diffs with minimal context)

So you either cycle through cursors (if your editor has a concept of "primary cursor") to see before/after or you do it blindly and accept a chance to be wrong

At least in e.g. Emacs and sublime text, you can mark all occurrences throughout the entire file. Assuming the matches are similar enough that the same motions apply even if you can't see the cursor, you can perform those operations.

Otherwise, as a sibling comment said, incremental search/replace is your friend.

You do a search/replace which has a similar function, although applied differently.