From what I understand, the little rubber bands help a ton but you CAN replace them with little strips of saran wrap or cling wrap to hold the parts in place ....
The typical method is to get your tube ready and centered inside of the large tube blank but DO NOT GLUE IN PLACE YET. You want to use a thin or extra-thin CA to do the gluing, and you will want to work quickly. Make sure you rough your tube up pretty well, to get full adherence.
Lay out your small parts and set them in place in the blank ... as many for the area as you can that is facing your direction, and put some thin CA over the area to help keep everything in place as you turn your barrel tube to access the next area .... if parts are wanting to fall out, secure them in place with rubber bands or saran wrap until the CA cures. If you are missing any parts, it may be possible to simply swap out that "color" of the design with colored epoxy instead. Once the epoxy is applied, you can cover that area with saran wrap to keep it in place as it cures. Make certain to "flood" the areas closest to the ends of the brass tube to ensure it bonds all the way around .... in the case of a design that is only in one area of the tube or one side, make sure you flood the sides to ensure that the glue goes all the way around to the back as well.
After all the parts are in place and secured, you will want to use a sanding disc and possibly a jig to keep it square in order to square the ends of your blank. Once it's all squared up, you can turn it VERY LIGHTLY .... possibly with a very very sharp skew using extremely light cuts, but the more accepted method is to just sand it to the proper dimensions. (sanding it down is not a cop-out ... sometimes there really just is no better way, especially with delicate tiny pieces).
Finishing .... you'll typically want to finish using CA, in order to properly bond all the tops of the pieces and fill in any last cracks and gaps in the design. Right before you apply the CA is your last chance to fix any issues with color intensity and do any other special effects you had in mind .....
An idea I recently had was to take some pearl-ex mica pearl powder and rub it DRY over the blank, and THEN apply CA over it and see what comes up ....