I think the current wording is enough:-
"When you score a critical hit, you get to roll extra dice for the attack’s damage against the target. Roll all of the attack’s damage dice twice and add them together. Then add any relevant modifiers as normal. To speed up play, you can roll all the damage dice at once.
For example, if you score a critical hit with a dagger, roll 2d4 for the damage, rather than 1d4, and then add your relevant ability modifier. If the attack involves other damage dice, such as from the rogue’s Sneak Attack feature, you roll those dice twice as well."
So the 'damage dice' that get to be rolled twice are the damage dice belonging to that 'attack'.
'Attack' is a defined game term, and means a game effect resolved by an attack roll (specific exceptions exist). You make the attack roll, and if it hits it (usually) does damage.
That damage is the 'damage dice' belonging to that attack. If, without any other roll being required, that attack roll directly results in more damage dice being delivered by that attack roll, then those extra dice also belong to that attack roll and are also rolled twice on a crit.
But some effects, while only being triggered by a successful hit, do not belong to that attack roll but to another cause (such as a second attack roll or a saving throw, or by ongoing effects that continue over multiple rounds), then those dice do not belong to that original attack roll that scored a crit, and therefore do not get rolled twice.
If an attack said something like, "1d8+3 piercing, plus 2d6 poison", then ALL the dice would be rolled twice because ALL those damage dice belong to that single attack roll that scored the hit. The result would be 2d8+3 piercing, plus 4d6 poison.
But if an attack said something like, "1d8+3 piercing, and the target takes an additional 2d6 poison, DC 13 Constitution save for half", then only the piercing damage belongs to the attack roll while the poison damage belongs to the saving throw (whether the save makes or fails is irrelevant) and so the poison damage here does not get rolled twice. The result would be 2d8+3 piercing, and the target takes an additional 2d6 poison, DC 13 Constitution save for half.
So the existing language is enough: the "attack's damage dice", i.e. "the damage dice belonging to that attack roll" (as opposed to a different attack roll or a saving throw or continuing effect) are what gets rolled twice.
No errata needed.