CSS transitions do not work when assigned trough JavaScript

To make transition work, three things have to happen.

1. the element has to have the property explicitly defined, in this case: opacity: 0;
2. the element must have the transition defined: transition: opacity 2s;
3. the new property must be set: opacity: 1

If you are assigning 1 and 2 dynamically, like you are in your example, there needs to be a delay before 3 so the browser can process the request. The reason it works when you are debugging it is that you are creating this delay by stepping through it, giving the browser time to process. Give a delay to assigning .target-fadein:

window.setTimeout(function() {
  slides[targetIndex].className += " target-fadein";
}, 100); 

Or put .target-fadein-begin into your HTML directly so it's parsed on load and will be ready for the transition.

Adding transition to an element is not what triggers the animation, changing the property does.

// Works
document.getElementById('fade1').className += ' fade-in'

// Doesn't work
document.getElementById('fade2').className = 'fadeable'
document.getElementById('fade2').className += ' fade-in'

// Works
document.getElementById('fade3').className = 'fadeable'

window.setTimeout(function() {
  document.getElementById('fade3').className += ' fade-in'
}, 50)

.fadeable {
  opacity: 0;
}

.fade-in {
  opacity: 1;
  transition: opacity 2s;
}

<div id="fade1" class="fadeable">fade 1 - works</div>
<div id="fade2">fade 2 - doesn't work</div>
<div id="fade3">fade 3 - works</div>

Trick the layout engine!

function finalizeAndCleanUp (event) {
    if (event.propertyName == 'opacity') {
        this.style.opacity = '0'
        this.removeEventListener('transitionend', finalizeAndCleanUp)
    }
}
element.style.transition = 'opacity 1s'
element.style.opacity = '0'
element.addEventListener('transitionend', finalizeAndCleanUp)
// next line's important but there's no need to store the value
element.offsetHeight
element.style.opacity = '1'

As already mentioned, transitions work by interpolating from state A to state B. If your script makes changes in the same function, layout engine cannot separate where state A ends and B begins. Unless you give it a hint.

Since there is no official way to make the hint, you must rely on side effects of some functions. In this case .offsetHeight getter which implicitly makes the layout engine to stop, evaluate and calculate all properties that are set, and return a value. Typically, this should be avoided for performance implications, but in our case this is exactly what's needed: state consolidation.

Cleanup code added for completeness.

Some people have asked about why there is a delay. The standard wants to allow multiple transitions, known as a style change event, to happen at once (such as an element fading in at the same time it rotates into view). Unfortunately it does not define an explicit way to group which transitions you want to occur at the same time. Instead it lets the browsers arbitrarily choose which transitions occur at the same time by how far apart they are called. Most browsers seem to use their refresh rate to define this time.

Here is the standard if you want more details: http://dev.w3.org/csswg/css-transitions/#starting