By default root has a job that runs all scripts on /etc/cron.daily at 4 40
Login as root, and type: crontab -l
Edit: Forgot to say, to solve it, just put your script somewhere else

And also, it must be taking some minutes to start because logrotate and slocate (actually, updatedb) are also inside /etc/cron.daily and they seems to be executing before yours.