A couple things come to mind. One is as Ken mentioned are you sure they are pressed in enough? Second is, could it be you took too much off the blank when you sanded the ends of the blank? Third have you checked the length of the tubes? did you use the right tube for the cap? If you have other kits of the same type are all the tubes of same measurement. Some of these kits especially these themed kits the tubes get mixed up. Sometimes they all use the same tubes but there are times when not. So that is a starting point.
I watched that video of that pen being made on the PSI site and I saw the person have a hard time pushing the cap onto the tranny and he really had to push hard so I believe you did not push hard enough. One thing that signals to me though, it is prone to crack the blank on the cap so be aware of this and take precautionary steps like filing the inner tube a little and using a flexible glue to glue tube in blank.