Once the Project has been approved and generated, it will appear on the Projects tab. If you're not seeing these newly generated projects, check the global/custom views for your Projects tab (global views are managed in the Admin window under "Applications") and ensure all applicable Project Types are selected for the views.
The Projects will remain on the Project Requests tab so you can create views for viewing project scoring/prioritization against incoming requests, but if you no longer wish to see Projects on the Project Requests tab, you can modify the PR tab filters to only show records that have not yet been converted to Projects.