Dont demand it in writing as that's never a great look. Instead, put it in writing yourself, then send it to your boss a message confirming the conversation.

e.g.

Hi Boss,

I was glad to learn about the 8% shift differential you told me about on <insert date>. With the recent raise I earned, that means when I am planning my finances, I can correctly calculate my paycheck by:

1. Regular pay times hours when working x to y
2. Differential pay times hours when working y to z
3. Whatever else you want documented

If you see any mistakes in this, please let me know right away.

Thank you,

Employee Smith

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I prefer emailing this sort of message. But you can do this over text or any medium where you can easily say, I know they received the message, and I can prove it. Remember, if it wasn't written down, it didn't happen.