Yes, it's true you're supposed to pay taxes for money earned in the year it was earned, not just when you happened to deposit the check. That has little to no bearing for this situation.
First, the money isn't available since it hasn't even been sent to you. Until you sign-up for the service, and provide a bitcoin address for the funds to be sent to your private key, they are not available. But more importantly, since you have no business relationship with the person giving the money, I would think the best characterization for the income is a tax-free gift (up to $14,000 per giver). But IANAL, and this isn't tax advice.