I start with a round blank. I turn the tenons first and cut the threads and then drill and tap. I turn it down last using a collet chuck. I have a mandrel for the section. I actually have a set of Hinze mandrels but the rods are too long, so I didn't use them. I may cut them off and try them. I really like using the collet chucks because they are secure and don't mess up the work.
Now I'm getting a bit confused - why make a tenon first if you are trying to tap female threads?
It sounds like your intention is to use dies to cut male threads on the outside (such as the barrel end where the cap screws on the outside and the section screws into the inside) and taps to cut female threads inside. If so - reverse the threading, do the outside threads completely first.
Then take a piece of larger diameter stock (I use 1.5" Delrin rod) and drill and tap it to make a screw-on collar. Screw this onto the threads of the pen barrel nice and snug, then drill and tap the inner threads.
This will reduce the flexing of the thin barrel wall as the drill bit and tap turn inside - it made a huge difference to the quality threads when I adopted this approach. (Also dramatically reduced the number of snapped-off tenons on my nib sections.)
