Obviously the starting battery switch is not wired to control the starting battery circuit. In what position is the "house" battery switch when the engine starts? If it is also Off then the battery is connected directly to the solenoid terminal. If not then you have the starting battery wired through the house battery switch. More of a concern would be to where is the alternator output lead connected to as you would not want the engine running with the alternator output in an open circuit. It is possible that a PO may have chosen to wire the starting battery through the house switch to have all in just one switch but that could lead to mixing of different type batteries which is also not desirable. Identify your battery banks and the types of batteries and follow the (+) wires to the switches; you should have the wire from the starting battery go to the starting switch and that from the house bank go to the house switch.