You don't need to wait at all. You could have applied bot at the same time. They make combination products that work very well in the insect control/fert side but don't waste your time with granular weed control.
Hire it out to a pro to spray your yard for weeds and in the long run if you have them take care of fert/insect/weed control you will be much happier! (Trugreen/Scotts does not constitute professional)
Depending on where you are in the Tampa area, I have a reference I can send your way for fertilization/pest control.