There is a thread describing how to use keys on the remote to turn hyperion on/off. Just search.
The leds staying on is normal behaviour as they only receive a command and stay in the same state until another command is issued or power is cut.
You basically need a script that sets all leds to 0 brightness and map it to a remotecontrolbutton.
Edit: Here is the guide describing remote setup. Simply searching the forum for “hyperion remote” would have done the job.