I am not sure but I think I get it; when I've cut my thread with the cutter the next seam does often have a little wad where the tails got sewed back down into the seam. Is that what you mean?
I don't think the cutter is working wrong, I think that's just how it goes when you have small tails left over. Larger tails hang out and out of the way, but the small tails have nowhere to go so they get caught up in the stitches.
Leaders/enders would solve that; chain piecing would solve that; pulling the tails longer would solve that... I just leave it and then when I'm cleaning up I use my needle-nose tweezers to tug the ends out of the stitches and I snip them off if it's something that'll be visible. If I'm quilting I always start as if I'm FMQ'ing and bring the bobbin thread to the top and pull it long so I can tie a knot anyway so it's not an issue there. If it'll be sewn over or hidden I just leave it; it doesn't seem to cause any problems as it's not really lumpy. If anything it's probably a nice secure "knot"!