Does factory reset deactivate Find My iPhone?

I’m pretty sure that means Find My iPhone therefore Can Not be on

Not at all... the hello screen is not related to Find My Phone or activation lock.

A factory restore does not disable Find My Phone. Only turning it off before the device was restored, or knowing the password to the Apple ID that enabled it.

When you’ve wiped your device, it should have popped the widow asking to log in to your Apple ID and disable Find My iPhone. Anyway, if you have doubts, why don’t you check the location using Find My iPhone service: https://www.icloud.com/#find ?

I went to my wife’s new phone and used Find iPhone and it did not list the reset phone Among her devices. So I assume that setting has been turned off On her reset phone? It is powered down and in the box.

Find My Phone may be off, but Activation lock may not be.

If she erased the phone first, either while in your hand or via icloud.com, and then removed the device from her account, activation lock will be disabled.

What exact steps were taken to "factory reset" the phone?

The check for activation lock can only be done during the setup assistant. It is a real time connection to Apple's activation server.

What you have described did not say whether you followed the steps correctly.

It is mechanically possible to reset a phone using iTunes without first turning off Find My Phone. The only way to be sure is to try and activate the phone again to see if the activation lock screen comes up.

Either device is turned off or on, if it was online once with that toggle on, it will be listed in your devices. So probably you're right, that setting is off on your wife's iPhone.