I just paid for my subscription with Steam Payment and had no issue, I was not asked to update my address or anything.

Are you using Steam Wallet or Auto-Renew to pay, if Auto-Renew, I would logout and restart Steam, the same if logged in to the Steam site, and then select on the MogStation "Steam Wallet" and when it loads up the site, select to "Add Funds" to the Wallet and then it should skip Square Enix's payment processor and be successful.