Hypothetically if a republican candidate got 90% of the vote in the southern states and won the popular vote but lost all the other states should that person be president? I don't think so.
No, he should. My opinions on how elections work don't change when the parties flip.
And part of the justification for this is that in the case you site, the person would need significant minority support in the rest of the country to win the popular vote. My only fear in that regard is a 3 person race skewing it even further.