If the contract stated that you are to get drip edges, then the time to put them on is before the gutters go on and in fact they are usually put on prior to the installation of shingles. However, with a starter course of shingles and the ice and water dam extending beyond the roof substrate, you are unlikely to have a problem. The drip edge would be additional insurance against a problem.
What bothers me is that your roofer skimped on a relatively inexpensive item, probably to save time. I hope he did not short-change you anywhere else.
What bothers me is that your roofer skimped on a relatively inexpensive item, probably to save time. I hope he did not short-change you anywhere else.