So, the new account holder would probably get a 1099-INT for interest income if this was money deposited into their account. Or, it could be a 1099-MISC in box 3, especially if this was a large non-money gift. (Open a new IRA and get a tablet computer, for example.)
The bonus to the referring member could either be interest on a 1099-INT, or other income on box 3 of 1099-MISC.
I actually just read an article about something similar last week related to credit cards that give rewards points, dollars or miles. The rewards that a cardholder earns from their normal purchases are not taxable because it is basically a rebate of the transaction fee (there is a 3 way deal between the cardholder, the card issuer, and the merchant, where the issuers charges a fee to the merchant, the merchant includes that in their markup, which the cardholder pays. The rewards are a rebate of that fee and is not taxable income.) BUT, a joining bonus (50,000 miles if you make X purchases in Y months, etc) is considered taxable income and customers are getting surprise 1099-MISC forms that they weren't expecting.
