This is not a situation where the two different companies are working together to try and create a sense of a larger shared world. In fact, if either of them could get the other to back off, they would. The thing is, Bryan Singer has designed a sequence that he feels only works with Quicksilver, and Joss Whedon feels that there is a pressing reason for Quicksilver to show up in "The Avengers 2," and so what we're going to see is a legally-negotiated stand-off in which we'll get two totally different versions of one character. While they may act like things are amicable in public, HitFix sources say otherwise.
Singer has just cast Evan Peters as Quicksilver for "X-Men: Days Of Future Past." He's shooting first, so presumably, he will win the showdown in terms of being the first to define the character on film. Marvel has larger plans for the character, though, and wants to use him for more than just one action sequence. The way the arrangement works, Marvel Studios cannot refer to the character as a "mutant," and they can't mention Magneto at all. Likewise, Fox can't make any reference to The Avengers in their film.
That means they'll have to either explain his powers in a different way in "The Avengers 2," or they'll just have to make no mention of his origin at all. At this point, there are so many characters in "Days Of Future Past" that it seems odd they'd end up in a pissing match with Marvel about who gets to use a character who, let's face it, 90% of the audience for either franchise has never heard of.