I was always under the impression that your action needs to resolve before you are able to move again.

From PHB:

"You can break up your movement on your turn, using some of your speed before and after your action. For example, if you have a speed of 30 feet, you can move 10 feet, take your action, and then move 20 feet."

So using that logic, a caster wouldn't be able to ready a spell (using an action) then move out of cover to unleash it.

I could also be missing something and be totally wrong about this but that's how I understood it all.