The output you are "generating" is also getting redirected because both the output you want to "generate" and the output you want to throw away (to >/dev/null>) are being sent to STDOUT (standard out).

The only reliable way to send output to two different places is to send it to two different places. You'll need to set up your script so that the output want to throw away is being sent to a different place, e.g. STDERR.

If you aren't sure how to do this, you might want to update your original post with a bit of your code showing how the third party script and your other commands are being called. Be sure to add comments indicating the parts you consider "generated" and the parts you'd like to throw away to /dev/null

Best, beth