That is correct. I think part of the reasoning is that promotions also give health (50 health if I recall). I seem to remember in Civ V for instance that people would attack, then promote after. This prevents gaming the system in that way.
Like you see in the picture, there should have been a prompt to say that a unit was ready to be promoted. Across the top of the unit card will also be an action to promote, but yeah, it is very easy to miss. I do like the fact that the game doesn’t nag me to promote because of the health restoration effect. Sometimes it is nice to save up the promotion, then burn it to burst heal when needed.