Confirmed. Reproduce: Go to SW and mount up on a flying mount on the ground, so you have ground speed(210), not flying speed. Then go into air. Movement speed does not update until you change subzones. So, fly around, you will see the instant you enter a subzone, such as Old Town, movement speed will update to flying mount speed(420%)

Looks like an OnUpdate while mounted is a solution, doesn't have to be crazy, maybe ever 3 - 5 seconds.

This appears to be a current limitation of WoW's API. To update it manually close and reopen the character stat frame.