The recipe in the link is for me a strange one, and the reasons are:
1. Assume it used egg white only (so it's an angel cake? I have no idea what's in the "Duncan Hines White Cake Mix", but there might be baking powder and egg yolk powder.) - during separating the batter, adding colors, putting the batter into pipes, and finally pipping, a lot of the air bubbles in the Meringue/whipped egg white (which are supposed to support the cake structure) might already gone - this might lead to a batter that is lack of necessary elasticity (sorry for my wording, I am not very sure if it's precise.) If you take a closer look of the photos in the link, the cake is cracked, too.
2. Another factor might be the baking temperature and time. Cake rolls are usually baked in sheet/shallow trays, and the thickness is much thinner. If the baking temperature is too high or baking time too long, the cake roll will crack much easier, too.
2. I personally prefer use Chiffon batter instead of sponge or angel cake batter to make the cake roll. Chiffon cake is reputational for its moist and soft texture, which is 100% relying on a fully whipped Meringue. Usually, there is no other rising agent in Chiffon cake recipe. A plain Chiffon cake needs very basic ingredients - cake flour, sugar, a little bit salt (to balance the flavor), milk, vegetable oil, eggs - available in most of the household.
Ah, now I sound like a sales representative for promoting chiffon cakes, haha, sorry sorry.
As the chiffon cake is usually much softer and more moist, when it cools down (very quickly) to the temperature, you can already spread whatever filling you want - whipped cream, jam, sour cream, etc and roll it. After that, let it sit and rest in the fridge for one hour.
It's easier to watch
a video, and maybe take a try when you want.
For the rainbow like cake, a sponge cake that uses extra baking powder and/or baking soda (need to work with acid ingredients) with higher liquid content might be a better choice.
