Grout, before base boards?

Yes you do not lay baseboards down before grouting tile. He has presented an issue where now he has to push grout under your baseboards so there isn't a grout "void" right at the baseboards.

And it could look good the first few months but shrink a little. It isn't the end of the world but he basically made his job much harder and made a chance of a sloppy install. You will for sure notice visually if there are voids right at the baseboard. Now he has to tape the baseboards to keep them from getting grout on them, it is hard now for him to clean up, and you still have the problem of getting the grout far enough back at the right level.

Side note: The only logical reason someone does this is that the person/tools needed to install the baseboards was only available then. Just doing this before grouting could take more time based on my comments above - to work around it - than to actually put them back up.

Because this person is lacking some common sense I would keep an eye on them. For sure do not allow them to caulk the bottom of the baseboard. Caulk will fail here quickly. Yes looks good for a month or two but will fail miserably after that.