Basically.
Phase 1: The campaign. This is where the producer/publisher is actively seeking pledges towards a certain monetary goal over a specified number of days. Pledges are collected based on "rewards" and their costs. Essentially you're choosing what decks you want & how many, and you pledge that amount to the campaign. This continues until the campaign period ends.
Its important to note that no money is actually debited from your accounts until the campaign period ends and the funding threshold has been met or exceeded. If the campaign doesn't raise at least enough pledges to meet the funding threshold, then nothing happens.
Phase 2: Production. Assuming the minimum funding threshold was met, this is the period in which funds will be debited from your account, KS takes their 10% cut, and the rest is forwarded onto the creator. The creator will then produce the product. This period is known as "hurry up and wait" to the backers, because its boring.
Phase 2.5: The survey. The creator will either use a backer kit or the native tools within Kickstarter to issue a "survey" to all the backers where you enter your shipping details, possibly order more products, and/or tack on any additional notes necessary to make your order right and whole and complete. The survey is a pretty big deal. When you get the email about your survey, complete it right then.
Seriously. Don't wait. The #1 reason people fail to receive their KS rewards is because they forgot to complete the survey or they made a typo on their address in the survey. Don't let this be you.
Phase 3: Fullfilment. At this point all rewards have been produced, and the creator initiates the process to ship them to you. This happens either by a vendor like ShipNaked (a curiously-named but benign fulfillment specialist) or - what's more likely in this case - the creator just does it themself, or with the help of a couple friends or family members. Often times you'll receive a tracking number during this process. If you receive one you can trust the tracking number itself, but never ever ever trust the arrival date that is estimated. KS reward shipping is notoriously slow unless the vendor packages and ships directly with USPS or UPS. FedEx is second longest. DHL seems to want to ship their product through the Panama Canal via duck before you receive it at your door.
Coincidentally, this is also the process in which babies are made.