If a boy feels like they're becoming feminine but don't want to become a woman does that mean there transgender?

Nope. It just means he's a feminine boy.

No, they are not necessarily transgender.

A transgender person is someone whose gender differs from that which they were assigned at birth, it's not that a trans woman is a boy who wants to become a woman so much as they were always a woman but were assigned the wrong gender at birth - important distinction. Some trans people are non-binary so they are not men or women, it may be the boy in question is gender queer in some other way rather than being a trans woman but may not fully understand being transgender yet or may be reluctant in defining where he is in the gender spectrum. It may be that the boy is just a feminine boy, cis boys can be feminine without wanting to become girls/women.