The cup of tea wouldn't have effected the results so don't worry about that, you had fasted from 7pm after your tea so the results still stand.
Provided you didn't do anything out of the ordinary last night like going for a 5m run then you do need to adjust your basal dose again to prevent the drop in bg, ideally your bg shouldn't fluctuate by much more than 1.6mmol when your basal dose is right, although nearer 1mmol is ideal. However never adjust your insulin going from one nights reading, do some basal checks tonight and if the same happens again then cut back as from tomorrow.
Good luck and Merry Christmas to you ArtemisBow.