Below is the offer details from the ATT website. Not positive but it appears you get the watch when you get the phone, since it specifies that if you return your phone within 14 days without the watch you will owe $199 discount price. If it was going through the same process as the Verizon deal, they would wait till after the 14 day return period to send out.
Offer details
Samsung Gear S2 Offer: Offer ends 07/21/16. Smartphone: Must buy any Samsung Galaxy smartphone on AT&T Next® agreement with qualified monthly wireless service plan (voice and data). AT&T Next: Requires eligible installment agreement and service. If service is canceled, remaining installment agreement balance is due. Down payment may be required. Tax due at sale. See att.com/next for details. Watch: Requires new 2-year wireless agreement with qualified service (add to select existing plans for $10/month, or minimum $30/month on a new eligible plan). Requires Samsung account, pairing with compatible smartphone (sold separately) with 1.4GB RAM, Android 4.4+, and Samsung Gear application for activation updates, application downloads and to route calls, text messages, and third party app. notifications from smartphone to Gear S2. Restrictions apply. For best results, connect with compatible Samsung Galaxy devices. For a list of compatible smartphones, please visit: samsung.com/gearS2. Early Termination Fee (att.com/equipmentETF): After 14 days, up to $150 on watch. Return/Restocking: If return smartphone within 14 days without watch, will owe $199.99 discount. Restocking fee $35 each applies. Limits: Purchase limits apply. Bundle pricing may not be combinable with credits, discounts, and offers.
GENERAL WIRELESS SERVICE: Subject to Wireless Customer Agreement (att.com/wca). Services not for resale. Deposit may be required. Credit approval, activation/upgrade (up to $65 each), other fees, monthly, overage, other charges, usage, and other restrictions per line apply. Pricing and terms subject to change and may be modified or terminated at any time without notice. Coverage and service not available everywhere. You get an off-net (roaming) usage allowance for each service. If you exceed the allowance, your service(s) may be restricted or terminated. Other restrictions apply and may result in service termination.