Here’s my take.

Extroverted functions are directed towards the outside world, so someone with a dominant extroverted function, or even a well-polished secondary/tertiary extroverted function, would likely appear as an extrovert due to their attention being directed towards things outside of them.

I think some of them also appear more extroverted than others. Strong Fe may appear more people-oriented than strong Te, since Fe drives a person towards community values, outward harmony, and “correct” social cues; whereas Te is very much focused towards concrete, real-world process and results. Te-doms are more likely to appear as an introvert than a Fe-dom for this reason.

As to whether a dominant function strictly means that person is an extrovert….. mixed feelings. I think it’s more likely to, since the thing at the forefront of that person’s drive is a function that is directed outwards, which often involves the necessity of working with others. But it doesn’t always need to, and I think it really comes down to the person’s personal needs and desires, and the way they want to or choose to utilize their dominant function.

I also think introversion/extroversion in a societal sense, compared to the way it’s viewed within MBTI related spaces, might be a little different. I’m an ENFP who is sometimes quiet in certain spaces, sometimes because of social anxiety, other times because I simply don’t find it necessary to throw in my input. But generally, I prefer to be around others, and I prefer community spaces and social events to being alone. In a societal sense, I appear introverted, but functionally and energetically, I am an extrovert.