Had a long chat with a Verizon rep to get clarifications. This is the third one I've talked to in 12 hours, but I think these answers are the most definitive and line up with the small amount of fine print on the promotion.
1) You must sign up for the 24 month device payment plan, you cannot pay for the device in full (even though the checkout process let me do this on one of my upgrades, and the first two reps I talked to said it was fine).
2) You must have the iPhone 7 active on the line for the full 24 months to receive all of the credits.
3) You cannot pay the iPhone 7 off early. Doing so will terminate the device payment plan agreement, and that agreement being active is contingent on your receiving credits. If you do, you will forfeit any credits you would receive in the future. So, even if you want to upgrade to a new phone next year, and decide to pay off the device in full to do so, you will not receive your credits.
4) Obviously, as others have stated, if you choose to upgrade without paying off the device you will not receive credits after upgrading either.
5) The credits will start on your third billing cycle for your device payments. So for the first 12 months of paying for your device you will receive 10 months of credits. That's roughly $271 of the $650.