If your neck has a flat slot, leave the tab on. Its to support the middle of the nut.
If you have a curved slot, just grind, sand, file, bite, or laser the tab off and it will fit the slot really well.
On vintage necks, the curved slot is the same as the fretboard radius... so you can lay sandpaper over the first fret position and lightly sand the bottom of the nut after you remove the slot, to clean up any wavyness, or to reduce the elevation of the nut slightly.
Most of the time, you'll need to reduce the thickness of the nut by sanding its edges. Last one I did was done all by measurement - with calipers, and it fit the slot really well. IOW, no trial and error in the slot. Just sand it till its "this thick" and you're good to go.
On the width, you'll have to remove a bit from each side. If the neck is unfinished, you can file, sand and polish it "in situ" (right on the neck). If the neck is finished, what I do, is get the nut into position and score the underside of each end. Thats my rough cut mark. After the rough cut is made on each side, I try it, make sure its ok, then measure the width of the neck. Sand or file the nut ends a little on each side so the width is the same or maybe .001 or so under. Done. Round the top edges a little to make it comfy and modify the slots (if need be).
The last black Tusq nut (used to be called Graphtech nut) didn't need its slots tweaked at all. I could have... and been really really anal on it. But it played and felt really nice as it was, so I left it alone. Used to be, you'd have to remove a bunch of material from the bottom of the nut if the slots were too high (and you didn't have files to lower them).