So after having read over the files on the contamination of clothing, only beta particles were found. No alpha nor gamma quanta. I'm going to make this explanation short and chop it up into two subsections for the sake of clarity because after some research it seems that most high school level explanations do so and I don't think this needs any more than that.
Note that alpha particles can be blocked by something as thin as a sheet of paper, beta particles by aluminium, and gamma rays can only be blocked using lead.
Basically, when the radiation is inside the body (inhalation or ingestion), alpha radiation is the most dangerous since it can't escape your insides and will be super easily absorbed by your cells. This is also extremely hard to treat, and has been used as a political weapon before (look at the poisoning of Alexandr Litvinenko). Beta particles, on the other hand, are a bit more odd. They're faster and more high-energy than Alpha particles but are much more likely to simply pass right through you if ingested, although there's still a possibility that it might be absorbed by some of your cells. Most people seems to say that beta radiation can be as harmful (if not more) than alpha radiation when ingested, so let's stick to that theory. The tourists' didn't really have much internal damage, so I think we can rule out beta particle ingestion.
When the radiation is outside the body, alpha is the least dangerous, but beta and gamma are most dangerous. Gamma radiation would basically pass through you at high levels of energy and can break DNA molecules. As such, gamma radiation is less measured by its adverse health effects but rather by the probability that you know how of developing cancer.
Alright, so beta particles, like the ones found on the tourists' clothes. First of all beta is a type of ionising radiation, which means that it holds the energy to liberate electrons from their respective atoms or molecules. Had the tourists had prolonged skin contact with beta particles we may have been able to notice radiation burn at the area of contact. Note that radiation burn isn't like a burn from a fire, but consider that a sunburn is considered radiation burn. I think that most likely the effects that they would have felt from the radiation were more than likely not instantaneous, but would have rather developed throughout their lives. Those exposed were at a higher risk of developing cancer and it would have most likely affected their reproductive health as well, so there's also a probability that their children may have had problems developing.
So as a small conclusion, the effects were unlikely to have be observable at the time of their deaths but would have taken much longer to set in. The only effect which would have been observable would have been radiation burn, and one can argue that "the odd skin/hair colour" of the students' might be a sign of this, but I think much more radiation would have been needed in order to produce that effect on the majority of their bodies.