I assigned both the pipeline controller and the component to this worker. Do I rather need to create two agents, one in services mode for the controller and then another one (not in services mode) for the component (which does training and predictions)? But, this seems to defeat the point of being able to run multiple tasks in services mode...

Yes. Again, the services mode is for special 'system' services if you will. The controller can run on the services agent (although not necessary since you can run the pipeline controller on any queue you'd like) while the steps themselves run on different queues