You need to add yourself to the crontab group.
usermod -a -G crontab (username)
Once you have done this, you also need to make sure that cron is running. Usually this is started with start cron however upstart does not work on WSL from what I can tell, but sudo cron does the job.
One caveat to this is that once you close all bash windows, cron will stop running even though your computer runs. However, as long as you have a bash window open and cron running, it will perform as expected.