I think most things that shoot bullets as projectiles count, I think I tried using the aegisalt pistols to unlock something once and they didn't work for me either. Sometimes weapons from mods aren't set up in a way that the specializations recognise, so if they don't work try another, think I just used random generated guns for some of them.

Also, don't shoot them from offscreen, when it says "within seven blocks" that's how close you have to be for the kill to count, you want to shoot things while standing right next to them, basically.

I believe Aegisalt weapons use plasma or something similar for their damage type, which is why they do not work. As Unadjectivable said, try using randomly generated guns from very close range.