To whoever it may concern,
The following is how I, personally, got a refund. According to Apple Support Forms, here is how you request a refund:
How to request a refund
- Go to reportaproblem.apple.com.
- Sign in with your Apple ID and password.
- If you see the “Report” or “Report a Problem” button next to the item that you want to request a refund for, click it.
- Follow the instructions on the page to choose the reason why you want a refund and submit your request.
Personal Update Regarding This Issue
In total, I have tried to purchase Premium  three times with Apple ID Credit (money redeemed from Apple/iTunes gift cards) after the switch from Roblox Builder’s Club to Roblox Premium. I’ve had to request a refund from Apple/iTunes once and the other two times Roblox granted me membership via customer support emails.
About a month or so ago, I reported this issue as a bug directly to customer service. (This time avoiding going through the billing department, etc.) As I understand it, their team has been made aware of the bug and I assume they are and/or will be following up with fixing this issue in future. If this issue is not solved, it may be time for multiple users to to file a complaint with the BBB (Better Business Bureau) for further action from Roblox.
Otherwise, I wish the best of luck to my fellow developers. I understand your frustration when it comes to not being able to purchase Roblox Premium with this preferred payment method.