According to Google:
I have come from the zoo would be Sono venuto dallo zoo.
So, Duo does really mean that you are describing your origin.
Interestingly, even the intrepid Google Translate refuses to translate "Vengo dallo zoo" as "I come from the zoo", instead saying "I come to the zoo" and then asking "Did you mean 'I go to the zoo'
LOL brave owl
"I come in peace" - the tiger that those crazy people took from the zoo an hour ago. He was returned. And the people paid the price. Right now they are in the tiger's stomach