Possible to reverse a css animation on class removal?

In addition to the answers here, please cache your $(selector)

So you pretty much do this var elements = $(selector); to cache.

Why?! Because if you use the code in the answers on this page as is you will ask the DOM for that same element collection ($('#item')) each time. DOM reading is an expensive operation.

For example, the accepted answer would look something like so:

var item = $('#item');
$('#trigger').on({
    mouseenter: function(){
        item.show();
        item.addClass('flipped');
    },
    mouseleave: function(){
        item.removeClass('flipped');
    }
});

Since I've written all this text, might as well answer your question using CSS transitions

I know you asked for a CSS animations example, but for the animation you wanted to do (a card flipping open), it can be easily achieved using CSS transitions:

#item {
  width: 70px;
  height: 70px;
  background-color: black;
  line-height: 1;
  color: white;
}

#item+div {
  width: 70px;
  height: 100px;
  background-color: blue;
  transform: perspective(250px) rotateX(-90deg);
  transform-origin: 50% 0%;
  transition: transform .25s ease-in-out
}

#item:hover+div {
  transform: perspective(250px) rotateX(0);
}
<div id="item"></div>
<div></div>

Another approach, rather than using display: none, is to suppress the reverse animation with a class on page load, and then remove that class with the same event that applies the normal animation (eg: flipper). Like so (http://jsfiddle.net/astrotim/d7omcbrz/1/):

CSS - in addition to the flipperUp keyframe posted by Blake above

#item.no-animation 
{
  animation: none;
}

jQuery

$('#trigger').on({
    mouseenter: function(){
        $('#item').removeClass('no-animation');
        $('#item').addClass('flipped');
    },
    mouseleave: function(){
        $('#item').removeClass('flipped');
    }
})

I would have the #item start out hidden with the reverse animation by default. Then add the class to give it the animation and show the #item. http://jsfiddle.net/bmh5g/12/

$('#trigger').on({
  mouseenter: function() {
    $('#item').show();
    $('#item').addClass('flipped');
  },
  mouseleave: function() {
    $('#item').removeClass('flipped');
  }
});
#trigger {
  position: relative;
  display: inline-block;
  padding: 5px 10px;
  margin: 0 0 10px 0;
  background: teal;
  color: white;
  font-family: sans-serif;
}

#item {
  position: relative;
  height: 100px;
  width: 100px;
  background: red;
  display: none;
  -webkit-transform: perspective(350px) rotateX(-90deg);
  transform: perspective(350px) rotateX(-90deg);
  -webkit-transform-origin: 50% 0%;
  transform-origin: 50% 0%;
  animation: flipperUp 0.7s;
  animation-fill-mode: forwards;
  -webkit-animation: flipperUp 0.7s;
  -webkit-animation-fill-mode: forwards;
}

#item.flipped {
  animation: flipper 0.7s;
  animation-fill-mode: forwards;
  -webkit-animation: flipper 0.7s;
  -webkit-animation-fill-mode: forwards;
}

@keyframes flipper {
  0% {
    transform: perspective(350px) rotateX(-90deg);
  }
  33% {
    transform: perspective(350px) rotateX(0deg);
  }
  66% {
    transform: perspective(350px) rotateX(10deg);
  }
  100% {
    transform: perspective(350px) rotateX(0deg);
  }
}

@-webkit-keyframes flipper {
  0% {
    -webkit-transform: perspective(350px) rotateX(-90deg);
  }
  33% {
    -webkit-transform: perspective(350px) rotateX(0deg);
  }
  66% {
    -webkit-transform: perspective(350px) rotateX(10deg);
  }
  100% {
    -webkit-transform: perspective(350px) rotateX(0deg);
  }
}

@keyframes flipperUp {
  0% {
    transform: perspective(350px) rotateX(0deg);
  }
  33% {
    transform: perspective(350px) rotateX(10deg);
  }
  66% {
    transform: perspective(350px) rotateX(0deg);
  }
  100% {
    transform: perspective(350px) rotateX(-90deg);
  }
}

@-webkit-keyframes flipperUp {
  0% {
    -webkit-transform: perspective(350px) rotateX(0deg);
  }
  33% {
    -webkit-transform: perspective(350px) rotateX(10deg);
  }
  66% {
    -webkit-transform: perspective(350px) rotateX(0deg);
  }
  100% {
    -webkit-transform: perspective(350px) rotateX(-90deg);
  }
}
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
<div id='trigger'>Hover Me</div>
<div id='item'></div>