As I have elsewhere written, I am not persuaded that the Jewish practice of keeping their days from sundown to sundown pre-dates the Babylonian exile.
The Biblical evidence for such an "inverted" measure seems to me to be strongest in the New Testament, whereas an unbaised or non-assuming examination of the OT evidence (as much as I have examined it) leads to my conclusion that originally days were measured from the time of one's "rising"--or from an arbitrary mid-night point, since different people rise at different times.
This is a convoluted way of saying that it seems to me that our duty is to follow whatever the local conventions of telling-time dictate, without raising questions of conscience too high. Be convinced in your own mind.