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.