There are other skills plumbers need aside from being able to work with water. One of the most common things that a drain leak on is fixing water lines.
When you get to the house stand if front of the toilet and locate the water shut off valve. Should be down below the toilet on the wall. Just turn it off (righty-tighty) completely and flush the toilet. All the water should have left the tank, well at least most of it. If there is remaining water line repair get it out with paper towels or a rag. The important thing is that no more water came in. If it did then your valve is not shut all the way or not working and you need additional help.
This so impressed me, that I thought, here is the man who might fix my sink problem, and I told him about my kitchen sink. The look on his face was priceless, as he said, "Ridiculous! Sinks don't leak if they're new." He even showed me what to do. He took out a big heavy-duty screwdriver with a big flat-head blade and showed me. "This is what's probably lose." He put the blade of the screwdriver in a notch the size of a giant screw head that was right in the center of the drain basket where the plug sat in.
Clean the hole in the gutter railing first. It must be free of any debris, so you may want to clean the entire drain channel using a proper cleaner. In this way, you will have a clean surface area which will allow you to repair the hole more easily.
Be certain that the bathroom exhaust fan vents to the outdoors, not into the house or attic. If the exterior vent dampers don't operate properly or water line repair don't seat well have them fixed or replaced.
For a newly installed icemaker, you will need up to 24 hours to let the machine function and cool down. A newly installed icemaker may not work until the ice mold temperature has dropped to about 15F - 16F degrees. If you have just added a water line to the refrigerator, it may take up to about an hour and a half for the machine to start working. Also, a newly installed water line may have air in the line. It can sometimes take a few ice making cycles to clear the line of air.
In short, the emergency plumber you hire should be from a reputable company. If you think that you can rely on him then you should look for another one. An emergency plumber should be skilled and should be able to deliver quality services to everyone.