Hair Flipping Up and Out

A: This sounds like a combination of styling issues and cutting technique.
Apart from that, the hair can be styled to help ensure straightness. You can use styling product, such as hairspray in conjunction with a flat iron to smooth the curves into a flatter configuration. Just be sure to let the pressed segments of hair cool before you comb through them or you'll just defeat your intended purpose.
You could also use a round brush in combination with your blow dryer to style the hair to curve under gently in the back as desired.
The main thing will be to practice these styling techniques until you're comfortable with them and can create the look you desire.
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See also:
Undercutting or inverse layering
Flat iron styling
How to blowdry hair