I'm not sure what the rule is, but I will say that I applied to three schools last year without directly contacting POIs and got no responses whatsoever. This year I've applied to two schools, had previous contact with POIs, and have gotten interviews at both of them. Now there are a lot of other factors involved - I feel my SOPs were much stronger this year, and I'm applying to slightly less competitive programs this time around, so who knows if the previous contact actually made a difference. Overall I feel like it's a crap shoot - if you've gotten interviews without making any prior contact, don't worry about it! Getting interviews is the hardest part, so you've already got a chance and your foot in the door. Good luck!!