Do your cron entries have 2>&1 in them? If so, this is telling it to send email only on failure. Cron usually sends email on success or failure. Most people don't want the successful ones, only wanting to know when it failed. Or they just send output to a log file to look at it later (or mail the log file after the job is completed).
To change where the email goes, either set it up that the output goes to a log file and email the results after the job is done to the different user, OR you can change the alias for user@hostname to send mail to
user@company.com.
Or someone can give another option -