There's a couple of different ways you can use the paintbox. Dianna Shyne, a great acrylic artist, actually just scoops out piles into her palette from the paintbox with a palette knife. She's not really dipping her brush into her paintbox. So you could scoop paint out with a palette knife and put it on your palette as you need to. I like to dip mine in more.
Overall I'm not worried about the colors mixing a little bit because I want my colors to mix to some degree. My paintings need to be harmonized and inter-mixing the colors is actually a good way to do that. It's up to you to determine whether or not you want to have your colors be absolutely pure or not.
If the mixed colors bother you try gently scraping the tops to clean up the colors.
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