Does it turn all the time: Yes, as long as the Clutch/Brake pedal is not depressed. Your problem is that the belt does not stop completely every time you depress the Clutch/Brake. Find the reason and you fix the problem.
When You depress the Clutch/Brake pedal the idler is pulled away from the belt removing tension on the belt, and several "tabs" stop the belt from rotating.
I would remove the right foot rest and belt cover first. Check the belt cover (first image below) to insure the belt tab near the front is 1) present and intact, and 2) is not bent too far away from the belt (it should be straight along the bottom line of the belt cover, and the "bump" be approximately 1/16-3/16" away from the belt when the Clutch/Brake is NOT depressed). Also make sure the Idler "belt keeper" is there (second picture below) and positioned correctly (one side should only slightly touch (or pinch) the belt when the Clutch/Brake is depressed).
Your engine idle speed should not be touched unless it is NOT currently spinning at ~1000-1100 rpm at idle. Engine speed should not effect the belt from stopping when the two tabs are adjusted correctly. The belt should always stop regardless of engine speed. Changing engine speed only masks the real problem.
Here's the manual for your machine:
http://www.mywheelhorse.com/graphics/file/Tractors/1-3745-3741_A-5241-1.pdf
BELT COVER TAB
IDLER PULLEY "KEEPER" TAB