I realized that Trigger Mastery isn't very descriptive. Seeing as the Sniping proficiency, which says "Range +1" doesn't actually add 1 of any unit to your weapon's range, but rather increments the range type of your gun by 1, I figured TM may act in a similar fashion, rather than adding 1 to the value of the nominal rounds per second of the gun. I did a search for a specific answer either way, and could find nothing, so I endeavored to test it.

What I found was surprising. Not only was my hypothesis (partly) correct, I found that the speed stat is actually not all that accurate, and Trigger Mastery doesn't even do anything for some guns. The game over-reports your actual RPS, and some of the supposedly different nominal RPS categories actually shoot the same number of rounds in a given time frame.

I have currently completed every mission up to, but not including The Baron Battle!, the last mission of the Captain rank. I have done some missions multiple times to grind materials, so I have a lot of weapons, but not all of them. I equipped the Reyder-46 barrel, the Tommy gun magazine, Hollow point ammo, the receiver I was testing, the Cure implant, and nothing else. I changed only receivers and proficiencies between tests. I held down the fire button for each of the Machine gun and Sub-machine gun receivers I had, with the Sniping proficiency on and then with the Trigger Mastery proficiency on, multiple times each, and wrote down the median time to fire the entire 50 round magazine in seconds to the nearest hundredth. I then divided 50 by that time to arrive at the measured rounds-per-second. After that I divided the TM value by the Sniping value, subtracted 1, and then multiplied the total by 100 to get the percent increase in firing speed from Trigger Mastery.

I did not test Assault Rifles or any semi-automatic weapons, because the time to fire the entire magazine is largely determined by how quickly or rhythmically you can press the fire button. I was unable to test the SPD 20 category because I do not yet own the weapon with those stats.

It looks like there are 4 actual values for the in situ attack speed of a weapon, excluding the possibility that there is a faster speed specifically to make the SPD 20 gun meaningful (seeing as SPD 16 and SPD 18 are exactly the same, I tend to doubt it). They are, as measured, approximately 8.5 RPS, 10 RPS, 12 RPS, and 15 RPS. The actual RPS is always lower than the nominal SPD. For a couple of the nominal SPD values on weapons (10 and 12), the Trigger Mastery proficiency will bump the gun up to the next actual speed category. For the rest it will do absolutely nothing to your actual firing speed. As mentioned before, there is literally zero difference between SPD 16 and SPD 18.

It is worth mentioning that all weapons with the same SPD value of those tested behaved the same way. I will not be providing a list of the weapons I tested, because I did it quickly and it would be a pain in the ass to check. If someone wishes to reproduce my results, they can be more rigorous, using less confounding factors (no implants or other parts, for example), and testing literally everything.

All-in-all, it looks like this proficiency is usually worthless. I'm sorry to be the bearer of bad news.

TL;DR: Trigger Mastery provides up to a 20% dps increase on automatic weapons with SPD 10 and SPD 12. On every other automatic weapon it does nothing.