This is an intermediate course, therefore supplies for the Watercolor Jumpstart class are assumed. The colors you used in that class are just fine, but the hues used by the instructor are below.
(This Pre-class lesson has no videos; the free Pre-class lesson for WCJS has more basic info on pencils including some video.)
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You can use whatever brands of paints you prefer; results may differ but I always encourage trying to use what you have first before spending a fortune on more supplies. I use Daniel Smith watercolors because of their quality, transparency, and lightfastness.