Access to first class is prohibited without a valid upgrade. By taking place in first class without an upgrade, you consented to receiving the €20 charge, and you will not be able to get it back. 

You were unlucky to be one of the first travelers (or maybe the first) the conductor checked. The other people could go away in the meantime without being checked.

However, you cannot claim anything back.

Do not just follow other people to first class if you don’t have a ticket for it. In case of a packed train and still space in first class, upgrade to first class before you enter it and take a seat. Otherwise you have to keep standing in second class, because you just pay for transport, a seat is not guaranteed. Standing in first class without a valid first class ticket is not allowed as well.

It is great the conductor came to check. Travelling first class without a valid ticket is very unfair to people who really do pay for it.

When being checked in 1st class with NS Flex, there is no need to leave or being sent away because you ‘automatically’ pay the € 20,00 correction fee.

It would be nicer if the conductor warned beforehand, so everyone without 1st class travel right had a chance to leave.

Giving a chance to leave.... that's too easy.

It would be nicer if the conductor warned immediately after the train's departure that you need the right ticket for the class you're in, not just warning just before the moment when checking the tickets.

Sounds like a bad idea because they will do the same tomorrow.

That's the default. You can only use 1st class with a 2nd class ticket with explicite permission.