You might want to post this over in the plumbing forum.

If he is venting the exhaust into the attic air space, that's bad. Even if there are attic vents (normally gable wall louvered vent panels, or a combination of soffit and ridge vents) in the attic that allow air to move through the space. If he has the end of the duct just pointing at the attic gable vent, that's no good either. The goal is to get the moist air outside the house, not to dump it directly in the attic, or dump it near the gable vent, where air currents can keep the moist air in the attic. If he is bringing the duct up into the attic, then continuing the duct laterally and running the duct out through the gable wall and installing a vent cap out there, then that's a good thing. I prefer the vent to be rigid metal instead of the flex duct, and I prefer the lateral run to be sloped slightly lower as it runs towards the gable wall. I use aluminum tape to tape all seams in the duct, taping both the seam that runs the length of each piece of duct as well as around the circumference where two pieces are joined together. This way if there is any condensate in the duct it runs out the vent instead of pooling and/or running back down into the fan. It's a small, but important detail. Personally, I prefer as few holes in the roof as possible. Mongo

It's pretty simple to check. All you need is a candle. With the fireplace not burning, light a candle, hold it next to the water heater exhaust hood, and blow it out. The smoke should be sucked up the chimney briskly. Now do the same thing with a fire in the fireplace. If the candle smoke moves away from the water heater exhaust hood, you have a problem. Solving that could be as simple as opening a window to provide make up air for the fireplace. The downdraft from the chimney when it's cold is because it's cold. There's a plug of dense, cold air being held in place by the damper. When you open the damper, if you don't have a chimney with a naturally strong draft (most newer chimneys don't), you'll get a downdraft. Use the burning newspaper to reverse the draft BEFORE you get your duraflame going.

Just to tell you where I am coming from on this - I wrote the book! (It's fun to say that.) "Residential Ventilation Handbook" It's been said pretty well already, but bath fans must vent all the way to the outside. Not just near an opening. Use insulated ducting to reduce the possibility of condensation in the ducting. Use 3 screws to attach the ducting to the hood. That will keep the ducting from turning or pulling off. Be careful that the screws don't interfere with backdraft dampers. (Cloth duck tape was made from the same duck material sailor's pants were made from. Not good at all for duct work.) If you can do it, transition from the 4" nozzle on the fan to 6" ducting. The flow will be much better. Point the nozzle of the fan in the direction of the exhaust hood. Air is lazy. It hates to make 180 degree turns. Here is a link that might be useful: Heyoka Solutions