That's tricky.
If we view the commissions as discounts, they are not taxable. "Normal" credit card cash back deals are not taxable because it represents a discount or rebate of the merchant fee charged by the bank to the merchant, and rebates or discounts are not taxable, they are just price reductions. (Of course, if you use the property in business, you must use the reduced or net cost.)
However, to the extent that the merchant is paying Rakuten for advertising, and Rakuten pays part of that to you, it's not a purchase discount, but a commission, and I think it would be taxable.
Since I don't know exactly how it works I hesitate to give a strong opinion, but your cash back probably is taxable.
Referral bonuses are definitely taxable because there is no way it could represent a discount on something you purchased.
