Their appearance could be a coincidence, especially since Japanese Stiltgrass seeds can be moved into an area on deer feet. The label on the Bayer product (if we are looking up the correct formulation) does not list either of those grassy weeds as those which it controls. Stiltgrass is an annual, so germination prevention in spring is the best long-term approach to control, aside from excluding deer if they visit your property. Dallisgrass is a perennial, but not easily controlled with herbicides; those that may work are listed here: https://extension.umd.edu/resource/dallisgrass

They would be using a a non-selective (and possibly systemic) herbicide for the existing weeds if it risks killing the turf as well. Such measures may be needed for tough perennial weeds which won't respond to many other options. It would be the equivalent in terms of localized lawn damage as simply digging the weed clump/colony in question out. The bare areas can then be repaired by overseeding.

Fertilizer would not have an impact on the weeds (except for maybe boosting growth), but if the lawn needs fertilization, a concentrated formula or liquid is not the recommended type. If it's been about three years or more since a soil test was done in the lawn, we suggest doing that first now; you have time to receive results before fall fertilizers would be applied. This will let you know if any pH changes need to be made to boost nutrient availability for the turf, plus what specific nutrients, if any, are lacking. See these pages for more information on fertilizing lawns and the MD lawn fertilizer law:

https://extension.umd.edu/resource/lawn-fertilizing

https://extension.umd.edu/resource/lawn-fertilizer-schedule-chart

https://mda.maryland.gov/Pages/fertilizer.aspx

Miri