The cupcakes in my photos are similar colors (I think) and I used Wilton's rose, violet, lemon yellow, and I mixed my orange using lemon yellow and no taste red.
I use Wilton gel icing colours. They are a gel and don't water down your buttercream. On my cake pictures there are butterfly cupcakes on there and the colours are pretty bright and that's all I used to colour it. If I want black I start off with chocolate buttercream and then add the black because then I don't need as much black gel to colour the icing. I hope I've helped.
You can make all of those colors with Wilton gel colors. Sometimes it takes a lot of color to get a particular shade. It looks like they used rose (not rose petal), sky blue, leaf green, lemon yellow, violet and orange.