It doesn't look like our traditional jaman. Our Jaman is Eugenia jambolana. If the leaves (crushed ones) smell like jaman leaves, then it must be Eugenia species. Anyway as Shakespeare said "What is in a name? That which we call a rose, by any other name would smell as sweet ".
I am very fond of Jaman. There are three main types grown here for ages. Jamni, a huge tall tree with small fruits, some quite tasty, fruits after the common Jaman. Jaman,the common one some are delicious. Raw Jaman, twice the size of common Jaman And now new introductions (hope to get them soon) XXL Jaman (Gulab Jaman) a very large fruit White Jaman
A very easy to grow plant of medicinal value. I have three plants growing in my house, two bear fruit every year.