I just got in from sorting one of that very model for a friend in the village.
It's now all working correctly, and she's happy.
The problem is that the "extender" has its own DHCP server, allocating IP addresses in the correct range but which are not recognised by the router. You get a "connection" but there's no internet (the router doesn't know you).
It took a while to work out what it was doing - because a device already connected to the WiFi without going through the extender would keep its IP and continue to work when it switched to the extender as we walked through the house. It was new connections that caused the hiccups.
The option to "turn off DHCP" in the main screen was disabled. Fortunately, deep in the undocumented bowels of the system was another "DHCP off" that did work.
The other pain in the neck was that it takes about ten to twenty minutes to finish "reconfiguring" after a reset, so experimenting becomes a process involving much drinking of coffee. I don't know what on earth it does that takes so long, but that's not my fault.
I would avoid pressing the little button - that seems to screw things up royally. Connect to the TPLink using your iPad or whatever, and try accessing as 192.168.0.254, ID and password "admin".