Seems to be a small point of conroversy as to wether the tape goes inside the bar or not.

When I worked in a high-end shop back in the day of Italian steel, it wasn't considered OK to push the tape into the bar. Doing so resulted in a bulge at the end.

Instead, one would cut the bar tape at an angle, starting it flush with the end and wrap up the bar. This resulted in constant tape diameter all the way up.

Then you would shove the bar-end plug thingy in. A wrap with electrical tape was OK, if it was floppy. The Cinelli ends were sized for this procedure.

-Z