@pled This is the kind of question I am accustomed to answering in another part of my life, so I had the information bookmarked! These products are labelled as safe for animals and pets when used according to directions. Your brain is undoubtedly reacting to the small as a danger signal, but unless fertilizers like these are stored in open bags where you might inhale it for a long time, no worries.

Turf Builder is a name brand for lawn fertilizer, and comes in a couple of versions. The ingredients, from the product data sheet are :
Scotts Turf Builder 32-0-4 contains 32 percent total nitrogen with 4.9 percent being ammoniacal nitrogen, 14.1 percent urea nitrogen, 11 percent other water-soluble nitrogen and 1.0 percent water-insoluble nitrogen. This product also contains 4 percent soluble potash, 7 percent sulfur and 2 percent iron. Nine percent of the product's contents contains slow-release nitrogen from methylendiurea, dimethylenetriurea and water-insoluble nitrogen.
Scotts Turf Builder plus Weed & Feed adds the herbicides 2, 4-D - 1.21% Mecoprop-p - 0.61% so require a bit more caution,

None of these is of particular concern except the herbicides - if they drift, they can be harmful in concentration
but are still considered safe for home use he amount when applied according to directions. The amount of pesticide is quite small, and watering it in prevents it from becoming airborne.

However, repeated close exposure to the fertilizer (as by landscape workers) can reveal sensitivity to some of the ingredients or binders in some individuals.

Of greater concern is spraying of pesticides or herbicides in hot weather (above 80-85 F) or windy conditions. This can result in considerable drifting of the aerosol or vapors, and can be quite irritating to sensitive lungs.

So your inclination to listen to your brain, then check things out was a good one.
Sue