I can't quote references right now but, from memory, I will say that:
1) a tritium based material was, used in watches until the arrival of Luminova (perhaps in the eighties)
2) it is indeed radioactive
3) the amount of radioactivity, however, was negligible and does not cause the watch user any harm
4) moreover, as every radioactive material, tritium decays with time, so any possible effect is now zero

The decay mentioned above is the reason why, in many old watches, indexes and hands show a darker color in the luminous dots. In my own cal 11 Carrera (1153S), what used to be a yellowish green is now gray, and only the index dots sport a faint luminosity.