New roof, old roof, the ice really doesn't notice. With all of the freezing rain followed by freezing temperatures and snow, caused the ice at the edge of your roof to become larger and larger and clogging up your gutters. As this ice begins to melt underneath it has no way of flowing into your gutters to be carried away. Since it is a "dam", the water begins to back up underneath your shingles, roofing paper, through the wood sheathing and into your house.
There is a membrane that is used for this purpose. It is used in place of regular roofing paper on the first and sometimes second row. It is self sealing and highly recommended in the northern climate. It costs a little more but your roofer should have suggested it to you. It can be retrofitted for the future, or you could install a heating cable for winter use.

I just remembered. If you click on the old BBS for this sight, scroll down to the date of 1/11 and look for "Not a good situation" from JayJ. He lists a sight from the U. Mass. that will also explain the situation and also offer some solutions, particularly on the insulation. Some of his thoughts are theoretical but worth reading.