Definitely a zone 10 or 11 plant. There are several types of eugenia, and possibly you have a surinam cherry. Honestly, I don't know how to take care of this plant. (and my family has such a plant in our backyard back in Asia) It's tropical, loves full sun, loves to be well watered but I just don't know about winter care. You need to go to the tropical forum for advise or check with a tropical plant supplier to see how to treat this plant while it's indoors. I suspect it will need some help with lighting during the winter period.

I wonder if this plant is actually 'Brush Cherry' -Eugenia paniculata. A very pretty small leave variety.

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Ankrara's Hobby Corner

This site is a great care resource.

Here is a link that might be useful: Care information budget plants