Do you have the stock radio or not? I think with the stock radio and cheaper aftermarket radios it will go up with the unit on, cd or radio doesn't matter. But with higher end stuff you'll get an amp remote and an individual radio remote. Then it will go down with the cd player going.
Did you make sure your seals were all good when you replaced it? I just converted my RS with a non-power unit and made it powered. I love it. Just make sure it's all tightend down well, grounded correctly, and your connections are good.