When an acid carbonate is reacted with a strong base, what are the products?

What do you mean exactly by an 'acid carbonate'?

Do you mean carbonic acid, ?

If so, the usual acid base reaction takes place.

Or do you mean metals with acidic properties bonded to carbonate? Like maybe aluminium?

Those will not react because carbonate is a strong conjugate base (as carbonic acid is a weak acid) and will not react to bases, but acids.