I have another brand of a similar jig and think getting the pins and tails exactly even is too much trouble. Make the slightly proud so they stick out a bit. Sanding is needed, but you can cut it down using a Japanese pull saw. These saws have extremely fine teeth that are not offset and have a knife like profile. So they cut incredibly smoothly without marring the wood around the pin or tail. They cut on the backstroke, so you pull them, which makes controlling them far easier. There are several types, but the one you'll need has a thin blade with no backer support. See pix. Once you use Japanese saws, you'll be spoiled for most conventional push saws. Don't push on a japanese saw or it may buckle on you. Let the teeth do the work.
The more I do, the less I accomplish.