As explained in this question on the English site, there is a distinction in English between saying "How did you know?" and "How do you know?"
When someone makes an assertion, the distinction between "how did you know" and "how do you know" seems to be that "how did you know" implies that the person in question is correct in their assertion. "How do you know" is normally an inquiry into the person's credentials, and often expresses that the assertion is incorrect and/or ungrounded.
How would you say these expressions in Japanese, and is the distinction made by tense, as it is in English? That is, are they "どうして知っていましたか。" and "どうして知っていますか。"?