Yes, although Talstar P Professional Insecticide will kill fleas, you still need to incorporate an IGR like Tekko Pro to break down the reproductive cycle. You can apply both at the same time.
Permethrin SFR and Talstar P should not be mixed together. You would use one or the other.
Talstar P (Talstar One) alone is good for perimeter treatment of general pests. For some pests you would benefit from mixing an IGR like Nyguard IGR with it. This prevents young insects (such as fleas, roaches, mosquitoes) from maturing into reproducing adults.
Talstar P (Talstar One) can be used for everything except grubs if you have those and not sod webworms. For grubs you would need a product like Merit in granule or liquid form. For mosquitoes the key is applying Talstar to the underside of leaves of trees and bushes. For fleas and ticks as well as mosquitoes you can also add an insect growth regulator like Nyguard IGR.
You do not need to water the lawn before or after an application of Talstar P and Archer IGR for fleas according to the product label. Just be sure you are using the correct amount of product per gallon of water/coverage area.