The Ask a Question Tile is special since it's out of the box. So it doesn't need an IFrame, which allows it to do the popover.
Two options could be, creating an action within the tile, which when clicked, opens a lightbox where you can put whatever you want. Basically, its an App.
Hope that helps,
Thanks for your help Scott. I was hoping there might be functionality built into the Jive SDK that would allow a custom tile to trigger a popover, even if located in an iframe. I'll try out your first suggestion. The second suggestion isn't quite optimal, since it will end up pushing around the content below it, but I appreciate your input on this.