What kind of card your deposit is supposed to go on is something that's not clear; but whether it's a checking account with an ATM card or a prepaid card that allows for "loading", most accounts associated with cards allow you to sign up to view your account online. Most also allow you to check your balance over the telephone.
If you go to your bank/card company's site you should be able to register and be able to access your account. Most financial accounts offer a way to have alerts sent to you by e.mail, so you could arrange to be alerted whenever a deposit is made.
From what I've heard, people waiting to receive a first check from SSI don't have any real way of knowing exactly when it will arrive (or be deposited on their bank card account). Once the first payment has been made, however, all other payments/deposits are scheduled to be in your bank account on the first of the month. If the first of the month falls on a weekend your deposit will show up on the Friday before the weekend. Apparently, there are times when it may show up a little early. The Social Security Administration sites says, "on or before the first of the month".
In other words, your deposit should go in on the first (or the Friday before the first if the first falls on a weekend). That's when to expect it, and that's when you can check your balance on your card account to make sure that the deposit has been made.
More information about the SSI program can be found at http://www.ssa.gov. That's the Social Security Administration's site, and SSI information can be found among the other Social Security programs/information.