His ultimate seems to scale incorrectly in general. Even just the base weapon damage modifier doesn't give the result it having a 1.7 times scaling factor would result in it having. On top of that, ballistic enchantment doesn't effect its damage either.
I haven't checked the other skills yet but there's a decent chance they are also bugged so probably should check those as well.
Edit: Confirmed that ballistic enchantment also doesn't affect the other abilities when you activate it so somewhere the weapon damage scaling isn't mapping correctly or something like that.
Edit 2: Yeah in general the scaling's don't seem to match the ratios the tool tips list, nor does it seem to be based on the damage of his actual default bullets instead (not that I expected it to be, just was my next best guess) so while the number does go up when you have more weapon damage, it isn't scaling off of any numbers I can find. It almost seems like there's a different behind the scenes number being accessed by the skills which makes figuring out why things aren't working more difficult but hopefully this thread is enough for yoshi. Basically no item passives seem to work and only the base weapon damage percent does along with in consistent in item values you may have that don't require some passive or active to be triggered. Even then, the increase in skill damage doesn't match the actual weapon percent I have which was very easy to check with the shotgun since it just has a 1-1 scaling ratio, though checking the math for his ultimate also showed the numbers not matching.