I think the output is by default mailed to root.

That only happens if the command run by cron sends output to STDOUT or STDERR and they haven't been redirected somewhere else (/dev/null is a popular choice :-) because cron doesn't know what else to do with it. That's not the problem here at the OP is redirecting both handles to /tmp/test.txt.

I was thinking that if for some reason the redirecting did not work, the error message mailed to the owner of crontab would contain some clues to solve the problem.

Update: A reason like black magic maybe ;)

Regards, Stefan