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https://www.apple.com/shop/trade-in

Get a refund on your purchase of iPhone XS or Apple Watch Series 4 starting at 12:01 a.m. on 9.14.

anyone know what this means?

It’s saying starting on the 14th, you can trade in any previous device that you own that is permitted from Apple for a credit towards the purchase of an XS or Apple Watch Series 4. If you Scroll down on the link that you provided, it gives you a selection of devices to choose from to trade in.
 
It sounds like you buy your new phone, and at the same time, tell them you're going to trade in your old phone. Then they send you a box to ship your old phone back. Once they receive it, they refund you your trade-in amount.

Am I understanding this correctly?
 
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It sounds like you buy your new phone, and at the same time, tell them you're going to trade in your old phone. Then they send you a box to ship your old phone back. Once they receive it, they refund you your trade-in amount.

Am I understanding this correctly?

Exactly
 
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