There are different types of radiation, and different sources release them at different strengths. Tritium (hydrogen-3) emits beta radiation (in this case, an electron) as it decays into helium-3. It does so with so little energy, that the electrons it gives off are blocked by the outer dead layer of your skin. These electrons don't have much energy, but it is enough to light up the phosphorescent coating on those vials. Electrons hitting phosphors is the same thing that makes an old fashioned CRT television work. So really, as long as the tritium stays inside the vial, it's no more dangerous than watching TV.
It's a different story if it gets out, though. Tritium is a gas and can be inhaled, or can combine with oxygen to make tritilated water. Both of those can be easily absorbed into your body. Your insides don't have a protective layer of dead skin cells to stop the electrons, so there is a chance that they could do some damage. You wouldn't get radiation poisoning from something as small as a single vial's worth, but it would up your risk for cancer by a bit.
Correct conclusion, wrong premise.
The three types of radiation, in order of decreasing energy, are Alpha, Beta and Gamma/X-rays.
Most Alpha particles (two neutrons + two protons) have an energy of between 3-7 MeV (Mega electon-volts) - though *some* have much lower and some much higher energies.
Beta particles (an electron) have energies of around 1 MeV - though again there are "outliers" that have much less and much more.
Gamma radiation (a photon, so has little/no mass) ranges from a few 10's of KeV (Kilo electron-volts) to 800 KeV.
Alpha is stopped by a sheet of paper or the outer layers of skin. It's energy is high, but so is it's size while it's velocity is relatively low. So, like pool table balls, it quickly strikes matter and sheds the energy rapidly. Very destructive but travel distance through matter limits damage to a small location. Dead skin is "damaged" but it's already dead and is going to be shed, so no harm is done. It is very injurious internally but there is not much danger externally.
Beta is stopped by a sheet of plexiglass, and can travel about 1-2 centimeters into tissue. It's energy is relatively high, and the fact that Beta radiation is an electron means that it can react to form free radicals. Not terribly dangerous externally but quite destructive internally.
Both Alpha and Gamma radiation are highly destructive of tissue. Alpha radiation is so indiscriminately destructive that it has no medical use, while Beta is used to target cancers and endocrine disorders.
Gamma is stopped by thick layers of lead. While it has relatively low energy, it's small mass and high speed allow it to travel through tissue, increasing the chance of collision and energy transfer the farther through tissue it passes. Gamma and X-ray radiations are both useful in diagnosis and treatment in medicine, primarily because little harm comes from their careful and proper use.
The Beta radiation emitted by tritium IS stopped by the glass vial and the phosphorescent coating (that glows). I've measured the radiation from tritium vials and it measures very close to background - that is, next to no emitted radiation escapes the vial. I've also tried to image a vial on a gamma camera where I've worked. Though a gamma camera is optimized to visualize gamma radiation and not beta, I could not detect the vial under the camera.
