Teensy is one of the recommended official Arduino library files. He is compatible with the Arduino software and library files, so the same Mega2560 program can be applied directly to Teensy with or without minor modifications.
To make the Arduino support Teensy burning, download TeensyduinoInstall.exe from the PJRC website and install it into the Arduino 1.8.3 installation directory.
Many are unhappy with that library. You probably can use it, you have to set the right serial ports anyway. I tried to improve that library and in the end I had my own code and nothing of that library was in it.
I suggest to use something better.
This is the best place to start:
@Koepel
The one by PerryBapp is a version that needs no library but generally I find that it takes a bit of more code for intense back and forth. Have earlier used it for a single page project and its quick to get going.
The next suggestion Easy Nextion Library is actually pretty simple with its Event trigger model. I landed on it by chance and now after your recommendation have started my first project with it.