"When did they admit to that?"
Translation:Kapan mereka mengakui itu?
You use "mengakui" when the verb is transitive and has a direct object, and "mengaku" when it's intransitive. In this case, "that" is the direct object. (It's not totally obvious from the English sentence because of the usage of the word "to", but you could just drop the "to" and the English sentence would still be valid and have the same meaning.) Since there's a direct object, "mengakui" is used.
If the sentence were instead "When did they confess?", the translation would then be "Kapan mereka mengaku?" since the verb is intransitive with no direct object here.