Translation:Are you drinking my coffee out of my cup?
I have heard from native speakers that the present tense can (at least colloquially) be used for the recent past. Similarly, 'did you' in English can be used for things that are basically in the present, particularly a response with 'did you drink my coffee?' or 'did you just drink my coffee?' immediately after the action.
German never uses the present tense to express the past tense, not even colloquially. (The only exception being the historical present which is a completely different matter). http://www.canoo.net/services/OnlineGrammar/Wort/Verb/Tempora/Uebers.html?lang=en
So, let me get this straight. The possessive article "mein" is in accusative case because we can say something like this logic...."Sie" is the one doing the action" and "Kaffee" is the thing being acted upon? And so "Sie" is the nominative? and "Kaffee" is the accusative? With that same logic, I'd construct the following: Du trinkst meinEN Kaffee aus meinEM Tasse?
Duolingo is not the right tool to learn the meaning of life ;-) I guess there's not much use in thinking too much about the actual content of duo's phrases. A lot of them seem to be generated automatically. Sometimes, reasoning about possible contexts is fun, though. What if I brought a thermos flask of coffee with me to work, put it on my desk and sb. not only stole my coffee but also took my cup out of the cupboard! I might be inclined to stress the double-theft by mentioning both incidents explicitly :)