Hi Laura! - When copying Tasks to other Projects, the original data should be copied over as well. If you select 'Clear Financial Data' when copying over the Task, that will change the Revenue Type to 'Not Billable'.
You can change your preferences in Setup > Project Preferences > Tasks & Issues. There you can set the default Revenue Type upon Task creation. Depending on how your Tasks are being created and copied, this could affect it.
Below are some articles that could help explain this a little better, however intended behavior of copying Tasks is to carry over all properties of those Tasks. If that's not the behavior you're experiencing, I would suggest creating a case for our Support Team to look further into if you haven't already.
https://one.workfront.com/s/article/Copy-and-Duplicate-Tasks-218695605
https://one.workfront.com/s/article/Tasks-and-Issues-Preferences-189854638?language=en_US&r=218&ui-f...