I did that offer a long time ago. As I recall, it took more than a month to get credit. Part of the reason is that Doubleday wants to make sure that you are not going to return your books and cancel the membership.
When you did the offer you agreed to purchase some additionals books over the next 2 years. I did that and discovered that the first selections of books I made didn't qualify for the requirement because they cost less than $13.49 each. Each purchase to meet the book purchase agreement must be greater than this minimum (it may be more now -- ask Doubleday).
They don't require you to wait until you complete the required purchases to give you credit, but they do want to make sure you aren't going to cancel. And if you decide you do want to cancel now, you just have to send the books back and won't have to worry about having your FC credit being reversed.
If you're trying to meet the requirement for your $5 bonus, the easiest and least expensive way is to do any one of the daily surveys (Offers-->Daily--> Survey site. My favorite survey site is Give Us Your 2 Cents. Be sure to clear your cookies and temp files before you begin any particular survey site. (Also true for any regular offer you try to do.)
When you do a survey, whether you qualify or not depends on your demographics. Don't be discouraged if you are disqualified -- just keep asking for the next one until you do. When you do qualify, keep the congradulations window open for at least 5-10 minutes or until you see the credit in your account. I usually have my account page open on another tab so I can click to it easily and refresh to see if the credit has come thru.
If the credit hasn't come thru in 10 minutes, take a screen shot of the congrads page, open up your PAINT software and click PASTE to bring the screen shot into the PAINT window. I usually add comments to help identify what survey site is involved; the date/time the survey was completed and the topic of the survey. Save this annotated picture to your shared picture library as a jpeg picture. Name it something obvious: FCPOCGUY2c102111 (for FusionCash Proof of Completion Give Us Your 2 Cents 10/21/11).
If you haven't received credit for the survey in a couple of days, submit a Support ticket to FC and attach this jpeg picture to the ticket.
On the Doubleday offer: if it's been longer than 30 days, send a ticket to Support and ask them to check into it. If you have emails from Doubleday that provide proof of completion of the offer and you are still a member of Doubleday, then send those along with your ticket. If it hasn't been a month, just be patient.