I've assembled several Princetons or its variations and have
not had any issue with the clip spinning around. In fact, I just pulled a few out of my storage box and inspected the clips. All were quite secure and could not be moved.
Keep in mind, this style clip has no tab to capture into a slot of a mating piece of hardware, so by design it can spin if the cap, clip, and pen blank aren't pressed firmly against each other. Some things to check to insure full contact between the blank, clip, and cap are:
1) Insure the pen blank has been milled square to the tube. If not the clip will not have full contact with the tube and blank.
2) Insure the cut edge of the tube is flush with the pen blank and has a flat surface. Dull pen mills can create a scalloped effect on the cut edge of the tube, creating high and low spots.
3) Insure the pen tube has no burrs which could hinder full contact between the blank and the clip. The same goes with the cap. I always deburr my pen tubes before assembly with a deburring tool or a countersink bit in a hand drill.
4) Insure the cap assembly has been assembled correctly. The instructions tell you to press the transmission coupler into the cap, then slip the clip over the large end of the coupler before pressing the entire assembly into the pen tube. If you hang the clip onto the coupler and then press both into the tube at the same time, the clip could slip onto the small end of the coupler and be captured between the cap and the step in the coupler, not the cap and pen blank. This is a remote possibility, but could occur.
You can easily pop the cap assembly back off the pen with a transfer punch and inspect the cap, clip, coupler, and blank. It might not be a bad idea rough up the bottom of the cap and both sides of the clip ring before you reassemble. I'd also put a little LockTite Red on the these surfaces at the same time. I'm not a fan of CA for this purpose, as it's too easy get this stuff everywhere and ruin the pen. LockTite will clean off if you have any squeeze out, but give you the same adhesion.