It sounds like you're trying to use your Battery Tender while you're also charging the car. I wouldn't recommend that, because the built-in 12v converter is also trying to output 13-14 volts at that time. If your battery tender is showing strange light patterns, it's probably a sign that it knows something odd is happening.
(BTW, you didn't mention which model you have, but the Jr only has one light and can't show both red and green at the same time)