Indeed you need to do them again. But you also have to rerun them after a merge anyway. The problem is that you can no longer see which commits that you merged where green before the merge. For example is very useful if the merge itself breaks the tests (uncommon but it can happen).
Instead of taking the branch <feature> and rebasing it, make a branch called <feature>.1 on top of <feature>, then rebase that, leaving <feature> in place.
That way all your references remain intact and you can compare CI results.
It's all trade-offs. The trade-off being that you maintain history by having copies of a branch around, while the dude trying to fix a bug doesn't have to break out the vodka bottle upon arriving back home. :)
