Hey @mdelp,
Firstly well done on getting something working with your setup. I am sorry to rain on your parade but I very much doubt you will be able to easily trigger js based animation using Animsition because it is designed to trigger CSS animations. You'll have all sorts of conflicts with both approaches trying to wrestle control of the element you try to animate.
Also, to rain even more, you will have to deal with AJAX or the whole page will reload every time you navigate to a different section.
You could, hijack the click, run a transition-out before triggering the navigation, load the new page, have the loading animation kick in then run a transition-out to reveal the new content.
But as you can see, it's a fiddly process of several steps... And you'll be reloading the whole page rather than just swapping sections of it.
I have heard of a JavaScript library specifically for page transitions - I have never used myself so, not vouching for it but it was a colleague who, like yourself builds all his sites off WordPress so, I know they would work together.
http://barbajs.org