While waiting for an answer on why the crontab event was not running something interesting happened: the script setup through crontab actually ran! It turns out that it seems to to be using the time of day without considering the summer time. That is, it is taking the time as a fixed time from UTC not considering that it is still summer time.
As an example, the task that was setup as:
52 13 * * * /home/username/my_script.sh
actually ran at 14:52 (that is what the clock at the top right corner of my screen said). Because we are still in summer time, I am concluding that cron actually looks at the system clock and ignores the fact that we have added one hour due to summer time. Using @Rohitt Vashishtha words: cron doesn't play nice with timezones.