In one of my previous vaults, I noticed that when my food was positive and my medbay was staffed, my dwellers were constantly at full health.
In my current vault, my food is positive and my medbay is staffed, but all of my dwellers are holding at their low health hours after an incident.
Best Answer
Dwellers will not automatically heal any radiation damage they've taken. Radiation damage is indicated by the red section of their health bar:
To heal radiation damage, you need to build a science lab and staff it to make radaway packs. Once you have a radaway, select a dweller with a red section in their health bar, then click on the radaway icon in the info tab.
The stimpack icon is the button on the right, below the SPECIAL scores.
If you're wondering how your dwellers took radiation damage, your water level probably went lower than what is required to keep your vault running normally (indicated by the vertical line that appears on your water resource bar). If your water level falls to the left of that bar, everyone in your vault will slowly take radiation damage from radioactive water.
Also, I want to clear up a misconception in the question: Dwellers naturally heal non-radiation damage, regardless of whether or not you have a medbay. The medbay allows you to make stimpacks, which you can use to heal dwellers manually. To do that, select a dweller with a black section in their health bar, then click on the stimpack icon in the info tab. The stimpack icon is the button on the left, below the SPECIAL scores.