Hi! I'm using a Particle Electron as a microcontroller with the turbidity sensor. However that board only has 3.3V pins, and in my use case I can't use the Vin pin since I'm not charging by USB. I figured this wasn't a big problem since the sensor will work with 3.3V as well, however since my domain (0-3.3) isn't the same as the one in the example at https://wiki.dfrobot.com/Turbidity_sensor_SKU__SEN0189 (0-4.5) I can't use the equation that converts voltage to NTU.

At first you'd think that you could just multiply all readings with 3.3/5, however I learned that the relation between 3.3V and 5V readings is not linear. E.g. if I take a measurement in clear water with 3.3V and 5V and then do the same in dirtier water, the differences between the voltage values don't follow a linear path. Note that I learned this by taking measurements with an Arduino that can supply both 3.3V and 5V. However, I won't in my real project be able to use the Arduino.

The only solution I can think of is to take multiple samples with 3.3V, and then with 5V, and then create a function to map readings done with 3.3V to a "theoretical" reading done with 5V. However I'm hoping that there would be a better (more correct) way to do this. For example is there a similar equation to the one in the link above, but for when you use 3.3V to power the sensor instead of 5V?

Actually, I'm not sure if it's possible to use this 5V module on a 3.3V platform. It is able to show the data, but it doesn't mean the output is correct. (I have inquired the PM and I will update this info as soon as I get responded.)
There is no equation for this. But I think you can test multiple times at different turbidity and draw your own turbidity and voltage characteristics.