it's all very confusing and the big box stores and big name brands (Scott's, Pennington, etc) make it more difficult.
Ideally you would drop a pre-emergent (I like Dimension) to prevent the germination of annual spring/summer weeds, such as crabgrass. Typically crabgrass emerges early spring, but you really don't see it until summer. The big brands add fertilizer for convenience and they can also charge a pretty significant premium for that product. If you're an average homeowner who does very little this is a good step.
However, you are on this site which means you aren't the average homeowner. Many of the weeds you see now are either perennials (come back every year from roots, rhizomes, etc) or they are annuals that germinated last fall. Just because they are currently alive (green) doesn't mean they are growing at their full potential. You'll notice that many of these weeds will take off about the same time the grass does, usually growing a different rate, typically faster. That is the ideal time to hit them with the correct herbicide.
Want to make it more complicated? The more surface area a weed has (the larger and/or taller it is) the more area it has to take up the herbicide and that typically makes the herbicide more effective. So you want to spray the weeds several days after your last mow, don't spray after mowing if you can help it. I typically wait a day or two to mow again. Surfactants are essential with some weeds (you can buy cheap non-ionic surfactant on Amazon) by allowing the product to "stick" better.
So you fertilized, no big deal. It does force top growth of the grass sooner, but it may also encourage the weeds.
Typically we recommend waiting to fertilize so the desirable turf can wake up and focus on root growth. Hence mowing 2x.
I ran out of time this late winter and had to buy dithopyr (dimension) with fertilizer also. It cost $35 for the bag. I was at Lowe's and later found Dithopyr without fert at a high percentage that will only cost about $10 to spread next spring. I mention this because you want to read for product ingredients. Plus even when we know better, we can't always source the product, or are willing to pay the shipping costs to get a granular product.
Sorry for the rambling post. I cringe when I hear ppl at Lowes and HD giving yard advise..