This screenshot gives a sense of the timeline.
Until 4 hours after closest encounter, the spacecraft isn't even aiming its antenna towards Earth - it's busy taking photos and aiming instruments at Ultima Thule during the very short viewing opportunity as it zips past.
Then the light-travel time delays our getting the report.
Check out the slow datarate for the downlink of all the data, how long it will take!
Sauce:
https://spaceflightnow.com/2018/12/30/new-horizons-ultima-thule-mission-status-center/