It depends on the punishment, how quickly the system reviews & punishes the player, and if other players reported the player before he or she was punished. If another player also reported them, they might get the popup and you may never be notified.
Ultimately, the takeaway should be to continue reporting behavior that breaks the summoner's code and let the system do its job.
But then move on. Out of sight; out of mind... as it were. Don't let toxic players consume any amount of your thoughts, bc that's how they win. They want to get under your skin. It's really none of our concern after we report. The occasional pop ups we get are meant to encourage us to continue using the system... not send us on a witch hunt every time a player wrongs us and we don't get a pop up about them.
You should take comfort in the amount of threads on the boards complaining about IFS punishments. Players who deserve to be punished will be punished whether you get notified or not. It just might not happen right away.