Within context of the X-Men movie universe, this is never fully explained.
In the comics, she has yet to ever exhibit this ability, but it is conceivable that she could in the future.
In the comics, some mutants have undergone secondary mutations, later in life. These secondary mutations bring additional abilities which are not necessarily just logical extensions of their original/primary powers.
Some notable examples:
- Emma Frost - gains the ability to transform into an organic diamond form. This ability is demonstrated in X-Men: First Class, but is never stated as a secondary mutation.
- Iceman - gains greater ability to manipulate ice and simultaneously switch back to human form
- Gambit - gains the ability to gently influence people through a hypnotic charm
- Beast - becomes more feline than simian
Sometime between the events of X-Men: The Last Stand and X-Men: Days of Future Past, it is possible that Kitty Pryde undergoes a secondary mutation which would enable this sort of time travel.