I do the same thing. I'll often start picking up bits of someone's accent as I talk to them. I used to live with a Canadian, and by the end of our conversations my prosody started to match up with his... Until his accent become more American, I suppose.
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I have lived in Louisiana, Tennessee, Mississippi, and more. I remember I spent one summer working on a ranch in Texas, and everyone made fun of my accent when I came back talking 'bout hawg huntin'. I can honestly hear differences in Georgia accents vs Tennessee accents vs Texas accents... It's just something you kind of start to pick up after a while.
Something I do think is funny is how every American-made ancient Rome or Greece or pretty much ancient anything movie uses British accents. Even the Turks in Aladdin (Ottoman Empire, here) had British accents. Americans just seem to view it as "the far off" kind of speaking, I suppose.