That plugin can't initialize elements that are hidden - I believe it has something to do with you can't calculate the height of a hidden element simply. A simple solution would be to initialize the element when you show it, so for example:
tab_element.show().jScrollPane();
Another option would be to use the autoReinitialise
option and set it to true. This basically sets up a timer that will automatically reinitialize the object over a set interval of time. But this is a bit of a waste, so I would suggest the first option.
Link to the docs on this very problem. http://jscrollpane.kelvinluck.com/invisibles.html