The 'age' of groundwater is typically taken to mean the time since the water became isolated from the atmosphere. Tritium is still be used since it is produced in the atmosphere in small amounts and it can be measured by low-level counting or by the ingrowth of its decay product He-3. The half life of tritium is ~ 12.3 years so it is good for young groundwater. I don't know why the article states a large range for He-4. I expect it is a mash-up of He-3 ingrowth from tritium decay and the subsurface production of He-4 from alpha decay of heavy radioactive elements (an alpha particle is a He-4 nucleus). Thus it can be used to estimate age of very old water.
Argon-39 would be very useful in age dating groundwater but there are currently only about 3 labs in the world who can measure it and radioactive counting needs a large volume of water. The atom-trapping method is still in early stages of development. That method will be a big breakthrough for krypton, too.
Chlorine-36 is produced in the atmosphere and at low levels in the subsurface, which complicates its use. It is also produced in nuclear reactors and by atomic bombs.
The methods can be very accurate but you have to understand and account for the different sources and reactions that can affect the measurements.