When you make an ADR, there is a place to mark special needs - including allergies. Do that, then reinforce it to your server. They will (should) ask if you would like to talk with a chef or if you're comfortable ordering off the allergy menu.
If ADRs have already been made, give them a call and have them added on. I believe you'd need to do this if your allergen is not listed as well.
I will say, if something is unusual (like a "histamine diet") or something like diabetes where the diet is not EXACTLY the same as everyone with diabetes (I've known several people with it, and each of them avoid different foods, so their needs still needed to be spelled out - much to the annoyance of one I know who fussed that her ordering was so difficult for the servers while my gluten-free "thing" was so simple), be prepared to meet with the chef and explain exactly what you can and can't eat.
But I've never had an issue with allergies and Disney.