If you followed all of the steps in the support article you arrived here from, then your phone should be properly prepared to trade it in. None of your data, or any association to your Apple ID, will be on it.
When you tap "Erase This iPhone," your device will prompt you to enter your Apple ID password for security verification. Once confirmed, the iPhone will erase everything, making it ready for a fresh setup. You can then power it off.
To verify that is back to its "out-of-the-box" configuration, power the phone back on. You should see the "hello" greeting screen just like you saw when you first got this phone. Once you verified that, you can power it back down.
The other thing you can check is to see that this phone is now "missing" in your Apple ID Device List. If it is still there, then something went amiss with preparing it for trade-in.
Ref: Check your Apple ID device list to find where you're signed in - Apple Support