A phone is a very useful “reader” however they are generally not the best a coupling unless you know exactly ( well pretty close ) to where your implant actually is.
VS
Did the installer say what made them sure it was installed?
The odds are that It is very likely sitting under your skin
It would be unlikely ( But still possible) that the NExT came back out with the needle or was pushed out of the wound during clean up etc. It has happened before.
It would be unlikely ( But still possible) That the NExT is faulty, and EXTREMELY unlikely that both the HF AND LF chips were faulty
Did you happen to buy an access controller with your NExT.
It has a pretty good read range and if you have a NExT in your hand, it should read it pretty easily and narrow down your search and at the very least, confirm that your NExT is under your skin
Having no photos or video is not unusual for an installer
Has your installer done any xSeries installs before?
Do you happen to recall the angle of the install? It should have been reletively flat ( Parallel ) with the skin, without experience, this would be difficult to tell if it was the “wrong” angle.
A slight downward angle more than “usual” could result in a deeper install than “usual”
Also, pushing the plunger without withdrawing the needle slightly can result in the implant taking a deep dive.
I suspect that you have a deep NExT, but purely conjecture on my part.
This isn’t a witch hunt or looking to lay the blame or “point the finger”, rather simply trying to help you find your “missing” NExT.
See this 
This is typical of Amal / Dangerous Things.
Personally, I don’t think DT are at fault here, and yet he has offered a replacement to keep you happy.
It is totally up to you of course, but I would reccomend buying yourself an Access Controller to confirm if you have a NExT inside you or not
Unless of course you have another reader you can try?
I would still also like to know:
- Your phone model
- how you are trying to use it ( Perpendicular to the antenna, testing duty cycle, moving slowly etc)
- What apps you are using
- NFC turned on
- Phone cover removed