In
this video, after Revival Blessing is used, the revived Pokemon isn't sent out until the end of the turn. On Showdown, the revived Pokemon is sent out immediately, as seen in
this replay. No updates between the original Revival Blessing tests and the video seem to have changed anything relevant, nor any between the video and now. It seems that when this behavior was being tested, Revival Blessing was used after all other Pokemon had already moved
Edit: It seems that ingame, if you revive your partner the same turn it faints, it brings it back in instantly. That's probably how the original tests got this behavior wrong