If you're currently watering to sprout the seed, in four days the embryonic roots are already popping. I'd adopt a very strict hands-off (feet off, in this case) policy in terms of meandering around on the lawn.

So if it were my lawn, I'd skip it for now and plan on fertilizing around October 20th. At that point, it may be time for winterizer, or you may just be on the second fall fertilization (so winterizer is fine, but the actual winterizer will go later).

Winterizer goes when the lawn is still green but has stopped growing. For me, that's Thanksgiving, plus or minus a lot.

But if you decide you just can't let it go and it's bothering you, either starter or winterizer would be fine for this round of feeding. Make sure to step lightly, don't slip, and try to set your feet down flat rather than heel or toe first. It looks silly, like something out of Monty Python, but really does help reduce harm to the newly-sprouting seed.

Thanks so much for your advice. Will wait until Oct as suggested.

Seeds contain enough nutrients that you don't really need to fertilize immediately. You're good for awhile. You probably should have seeded in early August. Keep that in mind for next fall.