Hello mates!
For those who updated to Teamspeak latest version, 3.6.0, and finding joystick\hotas\throttle hotkeys not working anymore: with latest version plugins need to be updated to be compatible and, yes, setting hotkeys from devices other thank keyboard is done thanks to a plugin, being not natively supported.
It’s curious that the plugin is developed by the same company that makes TS itself, but they’ve not updated the plugin yet! 
At least… Not on the official plugin repository! While waiting, they’ve published a pre-release version on a Google drive. You’ll find it here!!
This is the original forum thread from which all these info come from:
Cheers and have good flights!
Ibanez
P.S.: you can find TS3 plugins folder here: “%appdata%/TS3Client/plugins/”