No annulment would be required for a previous “civil marriage” where the person is a Catholic no matter if it was consummated or not. Your husband tells the priest he was “married” “civilly” via justice of the peace and that is enough to see the marriage is not valid…even if they “consummated” the marriage it still is invalid…even if they have 20 kids it still is invalid.
However- now that you know this you will have to abstain from sexual relations with him until your marriage is sacramentalized. Just go to the priest there and he should be able to help you along these lines that you are hearing in this forum. If he does anything different call the local bishop.
I am also curious on a side note here. If you are married civilly, to a Catholic… and you are attending RCIA- you will not be able to receive the Sacraments of Baptism, Penance, Holy Eucharist or Confirmation in your present state- civilly married to a Catholic unless you vow not to have sexual relations with him until your marriage is sacramentalized.