Yes, you can set the Projects, Task, and Work types as mandatory, using the TimeTracker configuration screen.
By setting the objects as mandatory the Users can check in to the Job/Project only after selecting the Project, Task, and Work types.
You can mark all the objects as mandatory or any one or two objects as mandatory using the TimeTracker configuration screen for tracking time.
Note: You might see different objects for tracking time in your org. That is because the administrator at your org might have configured the app to track time to other objects.