If you are setting the cook up via the mobile app using either iOS or Android, it should not matter. The count down timer will only start once the selected temperature has been reached. I almost always when starting a cook will pre-heat the water bath to the desired temperature, add the food and then start the program. If the temp drops, the PC will restore the water to the selected temp and then start the count down timer.
Yes for eggs start the time immediately. Eggs are one thing that are really time dependent. Getting a poached egg just how you like it may take a few tries. Some things I do id to always use the same size eggs and to have them at room temperature before I start. Hard boiled eggs are easier to time and after a while you can easily control how done yo want the yolk. For hard cooked eggs also cool them quickly in ice water to stop the cooking. You want to be there for eggs so I would not use any mobile app for them.