My 2011 had this same issue. Had the fuel pump replaced, problem still existed...then had the fuel pump relay and wiring changed out and haven't had a problem since.

 

Just linking this thread to another thread that I'm participating...mine is 2012 Dodge Durango R/T with 33500 miles...same issue...fuel pump running after engine shutoff...ran out of battery next day. Yes you could waggle the M25 fuse or pull/replace the fuse..though it's not a fix...it's a workaround.

https://dodgeforum.com/forum/3rd-gen...not-start.html

Looks like Dodge is going on the same direction as Ford...they know the issue..can't fix them.

 

In this case they can, it's probably a failing relay embedded in the TIPM. They have an updated TIPM with a fix, but are not replacing unless/until they fail. If it lasts until your warranty is up it saves them $1,100. The relay built into the original TIPM overloads and sticks closed, running your battery down, or open and refusing to start. May go intermittent before failing. There is a workaround of adding an external relay, but they won't do it until you start having issues, and by then it may be to late to avoid replacement.