You're two different individuals with different mannerisms, beliefs, tendencies and so forth... I mean, of course you may just as well have outright conflict with your dual. Nothing is for certain.

Hell, keep in mind your dual's 1st and 2nd functions are things you naturally suppress in you unconscious, so it's likely that you would encounter more frustration with your dual than your identical. And there's the intro-extro difference and it is probably difficult to settle such differences...

But the stuff I describe here will be problematic later down the line, what you probably experienced probably has little to do with socionics, but rather your own immediate interpretation of a physical situation that could have happened with anyone you know