Nachum Lamm posts: Keep it to yourself. Don’t enthusiastically yell out parts of tefillah, say something along with the Chazan (outside of singing) and so on. People should hear the chazzan (or ba’al koreh) and no one else.
And yes, this applies to "reminding" people in the middle of the silent of shemonah esrei to say Mashiv HaRuach, Yaaleh V’Yavo, etc. Often it’s more distracting than anything, and eventually it becomes so robotic that I know people who continue to "remind" months after the phrase began to be inserted.
In short: Let the gabbaim and chazzan do their jobs, and don’t "help."