Hey Alexusto, welcome to the saltwater hobby and welcome to R2R!
I believe you simply got caught in what I think is a slight marketing scheme. Nutri Seawater does include bacteria in it and they do claim you can add fish right away if you use it so why wouldn't you believe that? The fact is, even when adding this product or Bio-Spira or the like you should still wait before adding livestock. You need your bacteria to multiply and embed in your substrate, rock, decorations, etc. It isn't enough just to be in the water column. The tank still needs to cycle.
But, since you are already where you are you are doing the right thing by asking questions and by ordering the Bio-Spira. You can control ammonia for now by water changes if you have more of the seawater or a good salt mix, this is where you would add the marine tapwater conditioner by the way.
Good luck, keep asking questions!