Here are the dates on the current offer:
9/30/12–10/4/12, 10/19/12–11/1/12, 11/9/12–11/15/12, 11/23/12–11/29/12 and 12/10/12–12/13/12.
You must CHECK IN during one of the listed periods; only the check-in date matters. If you check in on September 26 on a single room reservation you are not eligible for free dining for any part of your stay, as it is outside the offer's parameters. You would have to have two separate reservations, one where you check in on 9/26 and check out on 9/30, and one where you check back in on 9/30 and check out on 10/3, and then you would be eligible for free dining only on the 9/30 - 10/3 segment.
The problem with this is that you have to buy at least 2 day tickets with the free dining package. So even though you bought tickets to start 9/30, you have to buy MORE tickets. If you split your tickets like this, the price is higher, because Disney tickets get cheaper per day the more days you buy.
One alternative is to buy tickets that cover the full stay with the first reservation, then buy the 2 day tickets with the second reservation, and just keep the 2 day tickets. They will not expire until they are actually used. Just make sure you do not put them in a turnstile to enter a park.