I think the overall mental health of a person can effect the intensity with which those natural emotional states are experienced, or what evokes them. I may get angry, for example, but I'm not so caught up by it that I scream and assault. Or at the very least, the conditions that would provoke me to scream and assault are very, very unlikely to occur in everyday life and I am generally able to recognize 'I am entering the state of anger' and take steps other than screaming and assaulting to handle that emotional state and the circumstances that are occurring.
Someone with a mental illness may not have that luxury - they may suddenly be 'in the middle' of an emotion, a very intense one, and the ability to step back and separate themselves from the emotion is not there. They may shift from one emotion to another very rapidly without understanding why. Their inhibitions may drop drastically. Handling that can be just maturity or practice, but it's easier for some than others, particularly if they were raised where things got expressed that way and there's no sense of self outside of the emotional state they are experiencing. It may be virtually impossible for some without medication.
There are broad spectrums on mental illness anyway. I wouldn't categorize someone who was 'emotional' as mentally ill, unless it was impacting their relationships, career, etc. leading to legal trouble and the like. At that point it's outside the bell curve of the norm and causing damage to themselves and others.