A voltage regulator is the SMD component with 5 pins.
A single mosfet has three pins, but sometimes a few mosfets are in a single SMD chip.
If you don't have a voltage regulator on the level shifter, you must apply both 5V and 3.3V to the module, or the level shifter won't work.
Your question was about the level shifter that you showed in the link. That is a different level shifter than the ones that I prefer.
I'm confused. You could make a photo of your level shifter with the wiring.