Tritium does produce very low energy x-rays through Bremsstrahlung (braking radiation). These would not usually be detectable with a Geiger counter unless very high activities were present. Not the levels found in a watch. You would need a NaI detector, designed to see low levels of photon radiation (gamma and x-ray), to detect Tritium in a watch. This is assuming there is enough Tritium to produce a detectable number of x-rays and the efficiency of your NaI detector. Not likely in a vintage watch with Tritium’s short half-life.
The short answer is that you are not likely to detect Tritium in a “vintage” watch with any radiation detectors unless you open it and take a sample for Liquid Scintillation Counting. If you have a Geiger counter or dose rate meter and get decent reading you have Radium.
So recently I had my TH Kirium of 20 years serviced and they replaced the tritium hands with superluminova. I didn't know after the fact I say t swiss made t on the dial so got them replaced back locally.
You can see the difference in the picture on the left, at full burst and on the right after 5 seconds, the glow on the tritium hands and the spare luminova hands.
Okay, so the Tritium hands and dial are actually on the watch, and the two photos below are the Luminova hands?
If that’s the case, then I wouldn’t be able to sort Tritium from Luminova from either the color nor glow. Do you have a photo that’s similar to the above, but after a minute?
Are you that they replaced the hands with Super Luminova?
I’m not familiar with the TH Kirium brand so I’ll defer to you - but they did an awesome job of color matching the two luminous variants!!
If Omega did this it would mark it much harder to tell new hands from old.