Photoshop Elements 12 and Premiere Elements 13 are standalone products. Each comes with an Elements Organizer, Photoshop Elements 12 with the Elements Organizer 12 and Premiere Elements 13 with the Elements Organizer 13.
When a matching version set of the two is installed on the same computer, the Photoshop Elements and Premiere Elements share the same Elements Organizer.
Consequently, you are going to run into a loss of integration perks by mismatching the combo.
One example...slideshows created in the Elements Organizer 12 can be gotten into the Elements Organizer 13, but only after accepting that 13 will change the slideshow format into its new format rather than retain the format of the pre-13 Slideshow Editor.
Please supply more details if you have specific Photoshop Elements Premiere Elements requirements.