By ‘May his tribe increase!’ the poet means that he wants more people to be like Abou Ben Adhem who should be ready to serve their fellow men.
He says this because he feels that the world needs more people with humanity and kindness who are ready to help and serve the people.
The central message of the poem is that we should be kind, humble and always ready to serve our fellow men because everyone is just a manifestation of God. God also blesses those people with his love who serves other people.