Roundup/Aerate and seed with TTTF?
Thats not the type of turf seed you want to use on an aeration and over seed after roundup. Honestly I wouldn't aerate and overseed with TTTF on an existing lawn unless it was already 80-90% TTTF much less a roundup and re seed.
TTTF does not spread and fill in like other varieties and needs to be applied very evenly and at a big rate...like 10lbs per thousand. There is a bit of non invasive blue in your mix presumably but still.
To answer your question, which fertilizer method you use matters not. Whats in the blend, does.
That being said. Hit it with starter fert now and make the next app high N.