In a portable pumping system when lowering the pump and drop tubes into the well, won’t water be forced out of the well as the volume of the pump and tubes raises the head into well? How do you deal with this occurring?

You are exactly right. As you insert a portable pump, if the formation itself is fairly tight or has a very low hydraulic connectivity, you will generally see some increase in the water level and then it will dissipate. If you are in a more transmissive formation, when you insert the pump you will possibly see a slight rise in the water level that will be followed by it dissipating. Once you start pumping, you are going to drop the head inside the pipe and the initial water level rise will be overcome as you initiate pumping and start the purging process.