The check-in date is all that counts. If the offer says it starts on the 10th, and you check in on the 9th, you are not eligible for the offer at all. The only way to really swing this if you must check in on the 9th is to book a separate reservation for the first night and then a free dining package that starts on the 10th, check out and then check back in again.
If you're good with continuing to stay offsite on the 9th, or with having a room-only without park tickets or dining for that one night, and then possibly changing rooms on the 10th, it will be easy. If you want just tickets for the 9th, you may be able to access your package tickets a day early, but that would require going to a Guest Services and getting the ticket issued separately from the rest of your package. There is a ticket sticky on the Theme Parks board with information about this. If you want a dining plan for the 9th, then you would have to buy a package with a one-day ticket.
Since you're staying offsite before moving onsite, what were you planning to do about park tickets before you moved onsite?
