Why don't you try turning a hardwood sleeve to fit over it?
Len
Seems to me that the jig that Rockytime made and showed is an ideal tool to use when assembling the Turbin.
The metal assembly tube (jig) that comes with the Long Clicker has too big a bore (0.37") and would slip down too far, marring the top outer surface of the pen barrel and the clip of the Turbin. Good idea .. would require a smaller bore tube (jig) but see my next comment.
Making a hardwood sleeve would require sizing the hole extremely accurately and is probably not practical because, as Rockytime said, the bulb on the push button is only a few thousands smaller than the top shoulder (boss) of the pen. I say this even though the Turbin assembly instructions recommend this method (although they don't say how to make the "press block" or give necessary sizes).
A hardwood sleeve is the recommended method for assembling the Sierra Click pen and works fine because there is no bulb on the push button.
Not every pushbutton pen requires a jig, but it is wise to be mindful of the delicate nature of the click mechanism in all of them when assembling.
An example of a pushbutton pen that does not require a jig is the PSI Vertex click pen. For this kit the external plunger is the last piece to be added (see PSI assembly instructions). Prior to adding this piece it is quite safe to press on the top end of the pen (before the refill is in) as the instructions implicitly assume.
Note to RKB: Thanks for pointing out that the refill tip can get "hung up" on the Turbin stylus rubber. I wondered/worried about this possibility.