Yes, the scientists did get hurt.
The early work on radioactivity was done by Pierre and Marie Curie. Marie Curie died probably of radiation poisoning.
The experiment that proved that a nuclear chain reaction was possible was performed in the University of Chicago in 1942, although it had been theoretically predicted earlier. This experiment involved heaping up a great deal of uranium 235 into a pile until it began to heat up from the fission, although there was not enough of it to actually explode, and simply removing some of it (by crane, for example), reduced the critical mass so that it was no longer fueling itself.
The next thing to do was get the fissionable metal into a small enough volume to generate a truly rapid chain reaction, by forcing it into itself with dynamite. This experiment was performed at Los Alamos in July of 1945 - the first atomic bomb. The physicists were a long way away when they set the dynamite off, because they knew that if it worked it would release a great deal of energy.