I had a 2013 Fusion too, but it never did that. But it was the LX, so just a step up from the bare bones model.
What I didn't like about it was the location of the key hole on the steering column. It was too low, so if you had anything else on the fob like another key, it would dangle right on top of your right thigh and bothered me the whole time I was driving. I eventually just took every other key off the vehicle key and dealt with it since it was so annoying.
Ours was an SE model that was upgraded to almost a Titanium model. My wife and I both liked the car, but it literally ate tires. We purchased it new, the first set of tires, lasted 10 K, all highway driven. The second set lasted less than 12 K. We put 6 sets of tires on the car, including the original set in 5 years.
When I took it into Ford, they said it was the tires, or the front end was out of line. Had a 4 wheel realignment, did not help. The district manager got involved, they put it on the machine and it tested out fine. I told them "take it for a drive, every time you hit a bump, the backend slides a little, and its wearing out that tires". Their response," it looks good on the machine." The local dealer did sell me one set of four new tires at costs, and we did not even buy the car from them. They knew there was something wrong with the vehicle, and even said "ford does not stand by their products", I asked them what should I buy next and they said a Toyota, they will tear it down and rebuild it, just to keep you happy and become a returning customer.
Last time I took it in, the gal asked me if I was still having problems, I told her I was, and she said "see that silver Fusion down at the end, it has the same problems, and ford refuses to do anything about it also.
A few months later we traded it in on the Camry. I doubt if I will ever purchase another ford product and the fusion was the 5th one we had bought.