If it is truly the over flow hose that you are looking at and not your low point drain, it comes out near the top off the tank and exits at the bottom of the tank. The purpose of the hose is that your tank does not expand too much and break the attach points. It is not uncommon to see water coming out of the over flow hose for several mins once it is full because the plastic tank will expand and bellow at the top from the force of the water entering the tank. Once the water is turned off the tank returns to its original position and continues to flow until the excess water is expelled. You should be able to see the top of the hose where it exits the tank.
