You might consider submitting this as a product feature idea so that others can vote-it-up and our devs might consider including it in a future release. Look for the 'Ideas' tab in the upper right of this page, to the right of 'Tableau Community'.
Now, you might not currently be able to assign a different color palette to each manager, but I've attached an example where the color palette is applied to each manager, by Associate and restarts at each manager. So you have different shades of orange for each employee under a manager. I've accomplished this by using an Index table calculation that applies a value(or Rank) for each Associate, restarting each manager, and assigns a continuous color palette on that aggregated index value.
Feel free to reverse engineer. If you found this helpful, or it does answer your question, please mark it as such so that others can find it quickly.
P.S. I updated this in version 9.3.5, so if you haven't upgraded you might not be able to open the workbook.
Tableau Online Deployment Advisor
Great idea. We are using SSAS so we're limited on what can be done within Tableau, but this might be something we incorporate into the model for this very purpose. That's part of the reason I am hoping it's something Tableau considers in a future release. I also posted this in the ideas section: https://community.tableau.com/ideas/6516 . I wasn't sure where to put it, so I took a shotgun approach.
Thanks for the help,