When I move to Rainbow do I still need all the colours in the garden to attract Rainbow?
No. As per the Wildlife Guide, it's attracted by the rainbow plant.
However, if you don't have other colours, all alerts will show for the rainbow plant, meaning you won't know if it's a rainbow chameleon coming. If you have all the other colours, only rainbow chameleon alerts will show for the rainbow plant. If you have all colours except violet, rainbow and violet alerts will go to the rainbow plant. And so on.