Moving sketch from Uno to Pro Mini

Example code for COZIR CO2 sensor works fine with an Arduino Uno, but not with a Pro Mini 5V (using external 3,3V supply for the sensor)

Example code at Application Note 128 - Arduino UART to Interface to COZIR Sensor

This is how the two hook up:

SoftwareSerial mySerial(12, 13); // RX, TX pins on Ardunio

I only see the "Demonstration" line via the Serial Monitor when using the Pro Mini 5V.

Shouldn't this work without any modifications?

I don't have a 3.3V Pro Mini yet...

Have you connected the grounds of the arduino and 3.3v power supply together?

david_2018: Have you connected the grounds of the arduino and 3.3v power supply together?

No, is that generally safe to do? How can I know if the two bottoms are at the same level (excuse the lake picture)?