"Start" is just a generic function that gets executed everywhere, so careful with it.
TNManager.player.data simply sets a variable. This doesn't get synchronized. It's only there for you to keep track of things, like adding a local reference to some custom player class. If you want to synchronize per-player data, do this:
1. When a new player joins a channel, have him TNManager.Create a prefab that has a custom script attached that has all the data you want sync'd.
2. Inside that script, sync what you need via RFC targeting AllSaved or OthersSaved.