According to the Dodge media site, Hill Assist was available on the 2013 Durango, but it was an option, so that doesn't necessarily mean your vehicle has it.
We published an educational story about Hill Assist technology here at AskPatty: http://caradvice.askpatty.com/ask_patty_/2014/07/how-hill-hold-or-hill-start-assist-technology-makes-steep-road-starts-safer-for-drivers-.html
Hill-start Assist (HSA) keeps the brakes on briefly, after the driver's foot is moved from the pedal, to easily allow “non rollback” on hills. Hill-hold technology essentially offers an “extra foot” to manual transmission drivers to help novice and veteran clutch-shifters better manage hills, but we're also seeing it more frequently on automatic-transmission cars as well. “As fuel-efficient CVT transmissions with low-creep torque and low internal friction become more common, so does rollback on inclines,” explains to Nate Berg, Manager of Vehicle Testing for Mitsubishi Motors North America. “Drivers of manual-transmission-equipped cars are better prepared for such rollback, but drivers of automatic-equipped cars can find it quite disconcerting,” Berg says.
If your vehicle is equipped with it, it's really not a feature you can disable, though you may be able to talk to your Dodge mechanic to find out more about it. If that doesn't help things, please find an AskPatty Certified Repair Shop at http://www.askpatty.com/search/?type=all&m=30&q=&keyword= and they can help you with your concern.