If not hyperfine interaction is considered, the only parameter that must be taken into account is the probability of radiation as a function of the direction.
The exponential decay is observed due to the basics physics of nuclear decay. A set of radioactive nucleus decay following an exponential behavior, being more probable at times smaller than before half-life decay time, and that is why at times close to 0 the the number of events is the greatest, and it decreases later as an exponential function.
As we know, probability of radiation is higher in the parallel direction of the nuclear spin. Then, if detector 1 and 3 are parallel to a nuclear spin, gamma-1 and gamma-2 detection is more likely to be detected in this configuration than in a perpendicular detector configuration, as it is in detector 1 and 2. That is why the number of events in 1-3 is higher than in 1-2.