But the risk association might very well be not so much the exercise happening while under immune stress but the processes that happen during recovery doing their thing while under immune stress. Usually immune stress means infection and we don't get to schedule our infections, so this distinction (exercise time vs recovery time) will be very much unexplored.
Young males tend to be more into performance-oriented training (competitive, or focused on metrics, or both) than other population groups, and with an actual infection it might even be that the relevant immune stress does not really start before more direct symptoms suggest taking a break. Could be as simple as shifting the "no sports" instruction that comes with the jab a few days backwards.