I thought "avec" was the correct translation for "with" and "au" was the translation for "or". Please correct me if I'm wrong.
The word for "or" is actually "ou," pronounced "oo." "Au" means "on" or "to," and when there is a main ingredient (tea) with something in it/with it (milk) you use "au" instead of "avec."
dictionary.com defines au as on or to. So I guess tea on milk means tea with milk. Certainly cafe au lait does.
in this sentence I think the word 'au' is used here meaning 'of the' so tea of the milk, meaning the tea has milk in.