Je suis à Paris depuis hier I’ve been in Paris since yesterday

6.3 Flirting Lesson: Extra vocabulary 
 

Yeah, this is one of those directly untranslatable things from French. Because the action continues in the present (you were in Paris yesterday and you are still there), they use the present tense.

People use this structure all the time to indicate where they live. «Je viens de Paris, mais j'habite à Bruxelles depuis deux ans.»

My translation: I'm from Paris, but I've been living in Brussels for two years.
A francophone speaking in English would tend to say "I'm from Paris, but I live in Brussels since two years." because of the way the sentence is formed in French. :)

The passé composé doesn't quite work in that structure because it indicates a "one-off" action, not a continuous state that is needed to indicate that you are still doing it. Keep in mind that your passé composé verb is «aller» so it would be more along the lines that you had been en route to Paris since yesterday. :)

However, you could modify it as «Je suis allé à Paris, et je suis là depuis hier» to indicate that you are now there and that you have been there since yesterday.

No wonder your tutor said to think in French and not English and then translate. The grammar is difficult enough and then I am a literal, too literal and inflexible person. When I start thinking in French like you I will have to celebrate with a banner proclaiming "je suis arrivé". Please dissect my grammatical mistakes. :-)