The wort MUST be circulating or the immersion chiller does a lousy job. That is, it works very slowly. And the whole point of using a chiller is to cool the wort as quickly as possible.
If the wort is circulating, then the hot water is in contact continuously with all of the coils, and it does not matter if the cold water comes in at the top or bottom.
If the wort is not circulating, the chiller cools the water next to the coils, and that cooled water is very, very slowly replaced with hot water by convection.