The email just said:
Simply deposit $20 or more into your TAB account between Friday 7th August and Sunday 9th August (inclusive), and early next week we'll load a $10 bonus to your account*. Too easy!
The terms and conditions don't say anything about it needing to be your first deposit just that you have to have received the email to qualify. I think it may have been my first deposit though as I opened it with a free $20 through some promotion ahead of the World Cup last year and can't remember if I put any of my own money in before this. Perhaps that's why I got the email.