By the age of this question there is a good chance you already have an answer, but I will answer here anyway for anyone that is searching this same question.
Stored Displays do not save versions, they work off the default version of the geodatabase. The version listed in the source tab reflects the version the current user is viewing, it is not saved with the stored display.
One way to accomplish what you want is to have your editors, at first, open ArcMap, choose their stored display, change to the version they want to be using, then save as an MXD. From then on they should launch ArcMap from that MXD and the version will be as they saved it.