Hm. Unfortunately fire isn't just my imagination, have a screenshot. Is it possible there would be any difference if it happens from a barrel?
Edit: From looking at the screenshot, Sam started Arcadi's mission on fire but when I loader the prior save the fire is no longer. Though replayed this mission and can recreate persisting fire.
So Sam was standing next to a barrel and an enemy activates it. He stays at least one turn inside fire. The guys finish one enemy. Sam goes out of fire with 1hp and heals. Then Arcadi finishes the second enemy. The battle ends before Sam's next turn.
The next I launch the next ally's mission (Elena's) right away and, yup, Sam is on fire on the start. Reloaded an autosave and launched the mission again - no fire icon. So it doesn't persist in save.