It seems to me, if a search warrant is issued, some may try to hinder the police and cause trouble. I don't think they're being detained, just restrained so the police can search.
I just read the order. It looks like this was just a continuation of another power the Supreme Court earlier granted to the government. The police can detain anyone while a search is being conducted without justification, in whatever manner they see fit. The police did not use minimal force since they could have addressed all the concerns pointed out in the ruling by simply making her stay in the back yard under guard.
It also looks like the 9th and/or her lawyers screwed up, as they should have addressed the issue that her detention went beyond the time necessary to complete the search, meaning she was just being detained not in conjuction with an active search. She might have won on that.
BTW, it turned out she was a legal resident, not an illegal alien.