You know I got a theory about this. I don't think Big Mom got the power directly from eating Mother Caramel.
I actually think this is a big hint about how Blackbeard was able to steal Whitebeard's fruit and what his crew is up to now. And clearly he didn't eat Whitebeard. What I actually think happens is that when a Devil Fruit user dies, the nearest fruit to their body becomes a Devil Fruit. In Big Mom's case she would've eaten the nearest fruit because she ate everything in the area.
For Blackbeard, he most likely kept a fruit on him when he went to kill Whitebeard, and when he covered Whitebeard's body all he actually did was eat the fruit he had with him, which had turned into a DF when Whitebeard died. That's probably also how Doflamingo ended up with Ace's DF, he was probably knowledgeable enough to keep a fruit on him in case a DF user died. Right now Burgess actually is just carrying regular fruit with him, so they can turn into Devil Fruits any time he kills a DF user.