Narrated Al-Bara’ (and he was not a liar):
When Allah’s Apostle said, “Sami`a-llahu liman hamidah ” none of us bent his back (for prostrations) till the Prophet prostrated and then we would prostrate after him.
Narrated Abu Ishaq:
If you can see the Imaam in front of you, wait for him to change his position fully, and then change yours. Don’t just follow the takbeers.
This Salah discipline teaches you life discipline as well. Always wait for your leader’s signal before going about an action. It’s called ‘following’.