Hm. Well if the shifter is marked as 3 speed that’s one thing out of the way. Dynasys just tells you the mech is definitely from the 10sp series.
Your best bet is to heave the mech off and find the model number (it’ll be FD-M then some numbers). Once you have that, Google it and check what your FD is. Shimano did make 2x specific 10sp fronts but I’ve never tried triggering one with a 3x shifter so I’m not sure what would happen. The action you’re describing wouldn’t surprise me though.
The actual pull ratios might be the same, but thay doesn’t necessarily mean that just because you can wind the limit screw in to make a 3x FD work with a 2x shifter you can expect a 2x FD to work as a 3x FD because the shifter has three positions.