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If there is a river in the province then you may get the river penalty...but you also might not. I have not seen any pattern to it. Sometimes the exact same scenario can lead to different results.
To find an ultimate answer to this question I approached Johan to ask what is really the deal with these rivers. "When does the attack penalty apply?" And I got the following answer:
Johan (translated myself, from Swedish): "If a river crosses your movement arrow"
(I put it in spoiler tags in case you enjoy it being a mystery )