I think you are onto something there. This motivated me to go look at the original Japanese text where they write, "...遅くとも１２時間後には利用することができます"

遅くとも is "at the latest", １２時間後 can be "12 hours later", the rest is "you can use".

So probably the correct translation is, "at the latest it may take us 12 hours to process, after which you can use it.", or "at the latest it may be 12 hours, after which you can use it."