As I understand the judge’s “emergency stay” order, they don’t have to be released but they can’t be sent back to their countries, either, pending further judicial rulings.
So if there continued to be new arrivals in the coming hours and days, they could be detained, but of course everyone should want that situation resolved quickly, I would hope.
I do not see why the EO should apply to existing visas & green cards, but I’m no lawyer or diplomat.
Think your reading is essentially correct. Assuming the NYT article posted here is correct (one never knows these days), I feel less stressed about the judges action.
So the malcontents out disrupting JFK can go home and get stoned, then wake up to find their muslim buddies will not continue coming in after all.