They force you to keep a "saved payment" on the website account page in order to purchase the premium in-game via the tomes menu. I really don't like it, and delete the saved method after I'm done. If their servers ever get hacked, then your payment information is leaked.
• Log in to your account in a web browser
• Add saved payment
• Go back to Tomes menu, purchase premium for the season.
edit: Added clarifying instructions.