I wonder if this is a game related issue. How exactly you did it?
At least Chrono Cross does fine following scenario:
Start game with CD2 -> Select "New Game" -> Game asks to insert CD1 -> Press switch ISO but select some other disc than CD1 like CD2 again -> game reports CD error and prompts again to insert CD1 -> Press switch ISO and give now CD1 -> Game starts fine
At least Chrono Cross does fine following scenario:
Start game with CD2 -> Select "New Game" -> Game asks to insert CD1 -> Press switch ISO but select some other disc than CD1 like CD2 again -> game reports CD error and prompts again to insert CD1 -> Press switch ISO and give now CD1 -> Game starts fine