The ping wheel menu will pop up without delay when using the ping during a turn input (either via mouse or stick on controller).
The ping wheel delay that is set in the options is completely ignored unless the player/camera is not turning.
My assumption is, that the mouse/stick input is intercepted the moment the ping button is pressed rather than when the delay to show the actual ping wheel is up.
This issue has persisted since the launch of OW2 and yet this bug has not even been acknowledged as an open issue.