Correct. Brown wire bypasses ballast when starter is engaged. If the ballast bypass is tapped from the yellow starter wire this will create a connection between the 6-9 volts at ballast and your yellow starter wire. In your case it seems like you get enough juice to make the starter relay engage at 1800 rpm:-)
Go back to OEM wiring and problem should be solved (unless the reason for the former owner to rewire the bypass was a faulty ignition switch).
Lars