Hi Joost,
I have come across similar scenario, where timesheet approval process is driven by action items.
Scenario: When timesheets are submitted, custom process gets triggered to validate a business rule and send action items to the PM's for review. PMs after review can approve/reject from action item.
I have tested above scenario in 15.5 New UI. Actions item or links in the notifications will redirect to Classic PPM and not to New UI.
Regards,
Praneeth