So, I just took some heavy wounds after an unlucky fight.
I went to the next temple and treated the most severe ones.
On the worldmap, if I hover over the medicinal supplies icon it tells me healing will take between 3 and 6 days.
However all wounds individually heal in 4 days at most:
Cut Leg Muscles (treated, 1-2 days)
Pierced Arm Muscles (treated, 1-2 days)
Pierced Leg Muscles (treated, 1-2 days)
Pierced Side (untreated, 2-4 days)
Injured Shoulder (untreated, 2-4 days)
Light Wounds (all 1-3 days at most)
Number of medicinal supplies is calculated correctly (7-14)
Attached screenshot and savegame but I doubt you will need it.
It just became dawn and I entered another town. Wounds apparently progressed on their healing and the tooltip updated (second screenshot).
It is now updated and calculates the day correctly.