My experience. Indian citizen with a U.S. visa.
Flying through Chicago to Dublin and connection from Dublin to Europe (within two hours in afternoon) - transit visa not required.
Flying back from Europe to Dublin. Connecting flight to Chicago is after 20 hrs. Arrived in Dublin airport at 4 PM. Cannot stay on the airport in the night as the airport is closed. Have to pass through immigration. Transit visa is required but do not have it. So, immigration office scolds and stamps an entry permit and warns not to repeat the case. Once the passport is stamped, left the airport, stayed at a hotel in the city centre, returned back to airport, passed through immigration and boarded the flight.
Had asked both the airline (Aer Lingus) and the Irish Consultate in Chicago before boarding, if I will need a transit visa on return. But no clear response from both of them.
Summary - You need a transit visa to travel through Dublin if you land in Dublin on Day 1 evening and your connecting flight is on Day 2 morning. You cannot stay at the airport (not even airside). The airline doesn't stop you from boarding the flight to Dublin if you don't have a transit visa, but once in Dublin you need to have it.