There are lots of previous postings on this site about removing adhesive residue. You might want to look back through them.
My dentist does not recommend brushing my gums (due to concern about interfering with the healing of my gums or changing my gums in a way that affects the fit of my denture) but does recommend swabbing my gums with moist or wet cotton. That is a gentle and safe way to clean gums (as is rinsing with salt water).
I find the easiest ways to deal with denture adhesive residue are: (1) suck on a hard candy (especially, citrus fruit or peppermint) or a piece of fruit; or (2) drink a diet coke or something hot (like coffee and tea); or (3) rinse with hot water. They all dissolve the adhesive (or, sometimes, make it sufficiently gooey that it can be rolled off). You should also experiment and see if you can use less adhesive. That way, you will have less adhesive clean-up to do. Lastly, for the sake of the healing of your extraction site, try to place the adhesive so that it doesn't get on your extraction site.
I have not experienced an after taste. However, I do find that, as the adhesive dries out during the course of a day, it becomes uncomfortable and causes a feeling of pulling against my gums (and I really don't like the clean-up or not being able to eat in the middle of the night because it's too much trouble to do the adhesive and then clean up after it). So, I set a goal of being adhesive free and, with the help of a soft liner, and after I got through the initial phases of gum shrinking (which seemed to take forever), I have achieved that goal. You might want to discuss this with your dentist.