Praying to a Buddhist deity for healing of someone

How do Buddhists look to deities such as Green Tara or the Medicine Buddha by saying prayers or mantras for another person? How do the deity and the divine operate or function for this purpose? I believe that there can be divine intervention of a divine source. How is it with these deities? When I send healing to another person through reciting a mantra to the Medicine Buddha for example? How does the thought get through? How is the Medicine Buddha or Tara a vehicle for my prayers? The sutras speak about the benefits of reciting Medicine Buddha mantras for oneself. What does it do in praying for someone else? Simply, does the deity have powers to heal that person in a divine way? Like through God or calling for the archangels to assist?