Twinned Phantasmal Force

[Flashy]

I've got a sorcerer with an illusionist bent in a party I'm DMing and I've been trying to decide how I want to rule the Phantasmal Force spell interacts with twinning metamagic. My gut instinct is that it creates two entirely separate copies of the spell rather than causing the two creatures to have a shared phantasm but I'm not entirely sure. I'm curious what everyone else would do.

EDIT: Posted to the general roleplaying forum by mistake. Flagged for movement to the 5e forum.