First of all, it is worth noting that a person could be both a tyrant and a “man of the people.” The two are not mutually exclusive. A person could act in tyrannical ways and yet be popular if they used tyranny to pursue goals that the people liked.
My own view is that Jackson was clearly a man of the people if we define “the people” as common, non-elite whites. It is also my view that calling him a tyrant is excessive. The idea that he was tyrannical is more of a partisan attack on him than an accurate description.
People say Jackson was a tyrant because he vetoed more bills than all previous presidents put together. They say he was a tyrant because he failed to enforce a Supreme Court decision regarding Indian Removal. They say he was a tyrant because he worked to require states like South Carolina to obey the laws passed by Congress. They say he was a tyrant because he destroyed the Second Bank of the United States.
The only one of these actions that can legitimately be seen as tyrannical is one related to Indian Removal, and even that was clearly in accordance with what the common white person wanted. Presidents in modern times veto bills all the time. Requiring a state to obey federal law is hardly tyrannical. Destroying the Bank of the United States was no more tyrannical than it would be if the Republicans were able to abolish the federal Department of Education. These were policy decisions that appealed to common people and that were simply tarred as tyrannical by Jackson’s detractors.
Overall, Jackson was clearly a man of the people and there is no clear evidence that he should be called a tyrant.