css transition doesn’t work if element start hidden

To understand plainly the situation, you need to understand the relation between the CSSOM and the DOM.

In a previous Q/A, I developed a bit on how the redraw process works.
Basically, there are three steps, DOM manipulation, reflow, and paint.

• The first (DOM manipulation) is just modifying a js object, and is all synchronous.
• The second (reflow, a.k.a layout) is the one we are interested in, and a bit more complex, since only some DOM methods and the paint operation need it. It consists in updating all the CSS rules and recalculating all the computed styles of every elements on the page.
  Being a quite complex operation, browsers will try to do it as rarely as possible.
• The third (paint) is only done 60 times per seconds at max (only when needed).

CSS transitions work by transitioning from a state to an other one. And to do so, they look at the last computed value of your element to create the initial state.
Since browsers do recalculate the computed styles only when required, at the time your transition begins, none of the DOM manipulations you applied are effective yet.

So in your first scenario, when the transition’s initial state is calculated we have

.b { computedStyle: {display: none} }

… and that’s it.

Because, yes, that’s how powerful display: none is for the CSSOM; if an element has display: none, then it doesn’t need to be painted, it doesn’t exist.

So I’m not even sure the transition algorithm will kick in, but even if it did, the initial state would have been invalid for any transitionable value, since all computed values are just null.

Your .a element being visible since the beginning doesn’t have this issue and can be transitioned.

And if you are able to make it work with a delay (induced by $.animate), it’s because between the DOM manip’ that did change the display property and the execution of this delayed DOM manip’ that does trigger the transition, the browser did trigger a reflow (e.g because the screen v-sync kicked in between and that the paint operation fired).

Now, it is not part of the question, but since we do understand better what happens, we can also control it better.

Indeed, some DOM methods do need to have up-to-date computed values. For instance Element.getBoundingClientRect, or element.offsetHeight or getComputedStyle(element).height etc. All these need the entire page to have updated computed values so that the boxing are made correctly (for instance an element could have a margin pushing it more or less, etc.).

This means that we don’t have to be in the unknown of when the browser will trigger this reflow, we can force it to do it when we want.

But remember, all the elements on the page needs to be updated, this is not a small operation, and if browsers are lenient to do it, there is a good reason.

So better use it sporadically, at most once per frame.

Luckily, the Web APIs have given us the ability to hook some js code just before this paint operation occurs: requestAnimationFrame.

So the best is to force our reflow only once in this pre-paint callback, and to call everything that needs the updated values from this callback.

$('button').on('click',function(){
  $('.b').show(); // apply display:block synchronously
  
  requestAnimationFrame(() => { // wait just before the next paint
    document.body.offsetHeight; // force a reflow
    // trigger the transitions
    $('.b').css('right','80%');
    $('.a').css('right','80%');
  });
})

body {
  width:800px;
  height:800px;
}

div {
  width:50px;
  height:50px;
  background-color:#333;
  position:absolute;
  display:none;
  right:5%;
  top:0;
  transition:right .5s cubic-bezier(0.645, 0.045, 0.355, 1);
  color: white;
}

.a {
  display:block;
  top:60px;
}

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<div class="a">A
</div>
<div class="b">B
</div>
<button>Launch</button>

But to be honest, it’s not always easy to set up, so if you are sure it is something that will get fired sporadically, you may be lazy and do it all synchronously:

$('button').on('click',function(){
  $('.b').show(); // apply display:block
  document.body.offsetHeight; // force a reflow
  // trigger the transitions
  $('.b').css('right','80%');
  $('.a').css('right','80%');
})

body {
  width:800px;
  height:800px;
}

div {
  width:50px;
  height:50px;
  background-color:#333;
  position:absolute;
  display:none;
  right:5%;
  top:0;
  transition:right .5s cubic-bezier(0.645, 0.045, 0.355, 1);
  color: white;
}

.a {
  display:block;
  top:60px;
}

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<div class="a">A
</div>
<div class="b">B
</div>
<button>Launch</button>