If you want to use white color only, you can use the barrel jack adapter delivered with the power supply to connect the “-“ output to the “white“ cable of the neon LED adapter and the “+” output to the “red” wire of the neon LED adapter.
After you press the neon LED strip onto the printed tree you simply need to cut the strip on one of its markers shown on the side of the neon LED strip. The tree is sized to hold the strip 1 way around with not much overhangs of the LEDs as shown.
You will need to add the above listed Step-Down module to power the ESP8266 with 5V instead of the 12V delivered by the power supply. The 12V is needed for the neon LED strip itself. You will need to measure the output voltage of the module with a volt meter and set it to 5V to avoid damage to the ESP8266.