Must a EU bank pay 500€ to the ECB, if I deposit 100k€ into that bank?
Banks do not make matching deposits into central banks, other than in a hypothetical 100% reserve system. As such, the answer is “no”.
What happens is that the private bank has a liquidity inflow, and it would need to find a corresponding asset, normally a money market instrument. The yield on that instrument is likely negative, but the “negative interest” is flowing to the seller of the instrument.