We had a similar problem in our top floor apartment with the light fitting filling up in the hallway. I havent seen heavy rain for a while yet, but did the following to try and prevent any further rains coming in.
1 - Check drain on the floor above was not blocked and removed any dirt and twigs. If you are on the ground floor, may be worth checking that the drain out the front of the above apartment is not blocked instead.
2 - Reduced the size of the roof vents for the extract fans.
3 - if the water is coming in below a stair case, check that the stairs are not slopping the wrong way and running backwards and there are no cracks in the corners to let the water in.
Hope this helps.