I have always applied it the same day and then started watering.
Must keep seed moist. It needs to be misted 3-5 times a day depending on weather.

"How have others done this?"

Because it's starter fertilizer, that's what it's designed for. Be careful on too much tho, if you're using a "seeding soil", it may already have fertilizer in it.

Since you are watering so much you lose a lot of the fertilizer nutrients due to leaching. Also new roots are extremely short, so a lot of the nutrients are unavailable once they move down a few millimeters into the soil. What I like to do is apply a half rate at seeding, and the other half after the second mowing.

I did not consider the soil in the starter soil. Maybe I will take the starter soil back and get regular top soil. I don't want to over fertilize.

You did say what type of seed you are using but if you live in Montana you better start soon!