You can pause a YouTube video with javascript by calling the the pauseVideo method, but this would need custom javascript added to the site and I don’t have any example code for this.
I once made a band site where videos were included in tabs, but instead of putting the video directly in each tab I used an image from the video in the tab content. Each image which was a link that popped up a modal window containing the embedded video and information about it. A similar UI might work for your scenario if it is appropriate as the modal would need to be dismissed before a different tab could be selected. The reason I made the video section like this at the time was not actually to stop the video when changing the tab, but that was a side effect to the main objective of including larger versions of the embedded videos than would normally fit in the tabs.
If this kind of UI is not appropriate, I would probably hope that most site visitors are smart enough to pause a playing video before switching tabs.
