If you got the TTF that had Fog on it at the time you were landing you have to either recalculate from that point to ADL and then to a alternate or recalculate your position to ADL and then to the FM period that it improves.
What if you don't have the TTF? We will have to wait and see what the time line shows but there is no
requirement to update TTF's if you departed with a valid TAF. If the crew considered that the safer option was to continue to ADL (if it had CAT III) rather than to divert to an airport OCTA and that they were unfamiliar with then they would be ok.