I've posted spies in all my cities with 15% Unrest, to see if enemy spies get kicked out. But I readily confirmed that spies cause 15% Unrest another way - I moved one of my spies into an ally's city, and saw his PO drop 15% on the spot. This was for an ally with military access etc., mind you (me Julii, them Brutii), so of course it'd work for worse relations.

It also helps explain why all of Spain has 15% Unrest even though I've long since annihilated Spain, Carthage, the Gauls, and Numidians - the only folks you might've expected to have (once had) spies there. If any spy can waltz in and cause it, even an ally, it makes more sense.