My guess is that a high minimum wage would incentivize employers to hire citizens instead of new immigrants. There are plenty of anti-immigrant Republicans, as Donald Trump and his current base have illustrated.
That said, it's still weird because it'll likely piss off the large donors. I understand that he's trying to take some of Trump's base using Trump's tactics, but the only reason that Trump gets away with it is because he's financing his own campaign and couldn't care less about fundraising.