It's kind of hard to "copy the way it was built" if they don't tell you what cement they used and you don't have any experience with that stuff.
So I took a closer look at the hose, and it seems to be a 2 layer design. Basically the outer layer looks like clear reinforced vinyl. The inner layer is opaque white, and I'm guessing some kind of flexible PVC.
I got the new jet today and it was as I suspected - no barbs on the fitting. The manufacturer put this together without clamps, and I didn't see the point in using clamps without barbs either. Now I don't know exactly which glue was used, "Rain-R_Shine" or "hot lava" or if there are any significant differences between them or the manufacturer (that's one thing I was hoping to get answered here, but oh well.) So I just used Rain-R-Shine. I didn't see any evidence of purple primer from the factory - maybe they used clear primer. In hindsight I suppose I could have primed the inside of the hose with a Q tip, but I simply put primer on the jet fitting and pushed the hose on and off it a couple times to prime both pieces. Then I just glued it together. It now looks like all the other ones and seems to be holding strong.
The fitting screwed in pretty straightforwardly, but it's kind of like a shower arm - it's awkward because you can't hold both parts at the same time and you had to tighten the fitting side underneath, not the piece on the tub side. The jet part on the tub side would hold still which is a good thing, but it had to tighten just right so the nipple faced directly to the right. I can see maybe some factory worker cracked it during installation by tightening it too much in an attempt to get it lined up.
Will do a leak test tomorrow.