Even holding the strands correctly, you will see a bit of the other color showing through, especially if there is a significant difference in the colors.
This is normal. You will get better at hiding the unused color, but don't get frustrated at making it perfectly hidden.
Crochet is naturally a "holey" craft and it just can't be completely helped, unless you are a super tight crocheter and then you fabric will feel super stiff like a board anyway.
Relax. You're not crazy!