When the level 9 warlock spell "Blade of Disaster" lands a critical hit the damage increases from 4d12 to 12d12, but if the critical hit button is clicked when using dndbeyond to roll for damage only 8d12 are rolled.

First, it's not just a warlock spell and second, your problem is because the critical hit option only doubles the damage dice. It cannot change based on additional effects caused by magic items(Like a vicious weapon) or spells(Like blade of disaster) to my knowledge.

Might be worth changing that then. Each spell/attack has a seperate critical hit button anyway. For spells that specify a certain number of extra dice to roll when scoring a critical hit it's a bit misleading when the crit button ignores this.

Quote from AndreasChris >>

Might be worth changing that then. Each spell/attack has a seperate critical hit button anyway. For spells that specify a certain number of extra dice to roll when scoring a critical hit it's a bit misleading when the crit button ignores this.

Just add an additional 4d12 and do the math. 

Eventually the dice roller will probably be able to account for this - but it is still in its infancy (still in beta) and has a long way to go. For now - as Halfastbracegirdle said - you'll have to do the maths your self.