Lets have you understand how the behavioral system works.
The basic foundation of the system is it punishes people based on consistency x severity. Meaning people can be punished for 1 game of extreme toxicity or many games of mild toxicity.
Think of it like a health meter in music games. When you miss 1 note (mild toxicity), the meter goes up a bit, when you miss a whole strand of notes (severe toxicity), your health meter rises up dramatically. If you consistently hit your notes at good or excellent timings (neutral and positive chat), then the meter drops.
Other people don't get to do whatever they please, everyone is subject to the same rules. Whether they get punished will be dependant on how close they are to the end of the meter and how severe their toxicity is.
Your report, if after the review is found valid, will move them towards punishment. They may get punished down the road, but unless the game you reported them in shows up in their reform card, you won't get a punishment notification. Keep in mind that the reform card only shows you 1-5 recent games as examples of acceptable behavior, so it is very possible that people got punished but you'll never know about it.
Also, there is no need to ask for reports, all reports do is to flag the system to review the game. If it found toxicity, then it will increase the toxicity meter depending on the severity of the toxicity. The system will return the same toxicity score regardless of how many reports a player receives that game, and more reports don't get people punished any quicker.