Can you provide more info on how you are setting up your Timeline/Playable asset?
The basic usage would be:
1) Create the Playable asset (like your "FinWizard") in your Project folder.
2) In your scene hierarchy, add the Playable Director component to a gameobject, and drag the FinWizard playable into the "playable" field.
3) Add a track on the Timeline window, it won't have any binding (the stuff you circled in red) until you tell it what you are targeting with the track.
4) Apply the binding to whatever you want the track to affect. Does this part work? Does it show the binding (aka E_C_Finwizard, instead of just saying None)?
At that point you should be able to run the game and the binding should remain there. At what point does it show None for your tracks? You're saying if you restart Unity that they show back up? If so something else is going on (bug, or outdated version of timeline or something possibly?)
Also just to make sure its clear, the Playable asset (FinWizard) itself does NOT store the bindings. The bindings are stored on the PlayableDirector on the actual gameobject in your scene. This is so that you can re-use the same Playable in different places/scenes if you wanted to. So if you set up a PlayableDirector/Timeline in one scene and applied all of the bindings, and then opened another scene and set up a PlayableDirector with FinWizard as the Playable, it will not have the bindings.
Let me know if any of this helps, and if it doesn't then if you provide more info I can try to help figure it out.
