Why is it jiný muž but poslední strom?
According to this: http://www.locallingo.com/czech/grammar/adjectives.html adjectives with a soft ending in the nominative singular get -í.
Yes, however the adjective "jiný" has a hard ending - d, t, n can have both endings.
Unfortunately I as a native speaker can't think of a rule how to tell which is which...
But jiný is not a soft ending adjective. It just belongs to a different class of adjectives. I recommend to remember the nominative singular as the "base form". It is also the form used in dictionaries.