St. Teresa was a mystic and a theologian in the sixteenth century. This was unusual for the times. She was declared a doctor of the church in 1970. She is famous for founding the Discalced Carmelites.
Her spirituality includes community. Even though she was a contemplative nun she focused on other people. One has to be practical besides being mystical. One's prayer life should foster the care of others.
Spiritual intimacy with God occurs in and through living one's life in genuine concern for the welfare of others. As a Lay Dominican, I would put it as my contemplation leading to action. My prayer life helps my apostolate. This makes perfect sense to me. Before Saint Dominic founded the friars, 800 years ago, the first thing he did was found a monastery of contemplative nuns. Prayer came first. Then comes action.