In order to explain the last stanza, let's take a step-by-step approach.

A woman's life is her own
until it is taken away
by a first, particular cry.

Here, Stevenson is saying that a woman's life is her own until the day she hears the first cry of her newborn.

Then she is not alone
but a part of the premises
of everything there is: 
a time, a tribe, a war.

The birth of a woman's baby confers on her new responsibilities beyond the dictates of her ego; she must now adjust her worldview to take into consideration her new maternal status. Suddenly, she is compelled to take note of the larger world and to understand her part in humanity's history. She is 'not alone' anymore, but plays a part or is a factor ('premises') in earth's fate. 

Every new life continues mankind's struggle to achieve, to build, and to develop lasting and meaningful legacies. Whether she likes it or not, the new mother must contemplate her place in the larger sphere of humanity and her response to societal expectations ('tribe'), the decisions that precipitate conflict ('war') and the unique challenges of her era ('time').

When we belong to the world
we become what we are. 

In seeing herself as part of the world and in realizing the significance of her new status, the new mother begins to understand how she affects the world. Individualism is subsumed by initiative: in acting according to her best judgment and in working for the best interests of her child, she develops her sense of self. In other words, she becomes who she is by the decisions she makes as both a mother and a citizen of the world.