Buddypress: adding a new tab direct user to their author page

In your screen function ibenic_budypress_my_posts create a redirect.
Something like:

function ibenic_buddypress_tab() { 
    bp_core_new_nav_item( array( 'name' => __( 'My Posts', 'ibenic' ), 'slug' => 'my-posts', 'position' => 100, 'screen_function' => 'ibenic_budypress_my_posts', 'show_for_displayed_user' => true, 'item_css_id' => 'ibenic_budypress_my_posts' ) ); 
}

function ibenic_budypress_my_posts() {
    $url="/author/" . bp_get_displayed_user_username();
    bp_core_redirect( site_url( $url ) );
}