>> "Can someone explain what is going on, the field should get updated locally right?"
Yes, presuming 24 hours has really elapsed. Faking it (changing time, date, etc.) will likely trigger the fraud detection algorithm and get inconsistent results.
>> "Is there a way to see that my client successfully contacted the server?"
Yes, TA_OK means it successfully verified either locally or on the server. For more information about the best way to get updated custom license fields to end-users, see our extensive documentation on the subject: https://wyday.com/limelm/help/license-features/#change