M,
The two sources can not be connected together before the two auto-valves. The two valves can not be run at the same times under different programs. You might ask a controller rep if youcan run a pump under one program and not under another. You should have a backflow preventer on the municipal water side for insurance that will not let well water find its way into and contaminate your house water or others in the neighborhood. Does the water tank have sufficient water volume to handle a full peak irrigation cycle? If it does do not have the controller regulate the off/on of the pump but use float valve switches in the tank to start and stop the well pump. Have a low float valve switch to start the pump and high one to shut it off. JMHO Aloha

Thank you for your answer. The tank has enough water. I do not understand how to control the pump to start when the sprinklers have to work without using the controller. Could you please elaborate, Thanks.

This would take some electrical work to run a float switch between your pump and your pump relay switch. I liked this answer from someone else's similar question.

"If you need to control a pump, you will require a float switch which in common form has a set of switch contacts operated by a float. These can be top or side mounted and are available in different patterns to suit the application. A convenient side mounted unit is manufactured by Robert Mobrey where the internal float is not directly connected to the external electrical switch but operates due to the magnetic action of the float on the switch through the wall of the tank. Electronic level control sensors are also available. The pump can be directly wired to the float switch vai the mains supply or if high duty exceeding the switch rating or a three phase pump, via a contactor or relay."

If you have an technical background or you have a friend with one you can research the net and see how you can be incorporated into your set up. Otherwise hire a irrigation contractor to do it for you. The pump will only run when the tank empties to a certain level and shut off when full again. The only requirement of this scenario is your irrigation controller needs to be timed to irrigate only when the pump is full. I don't know if I answered your question but if you described the details of your pump and how your pump is wired up, I could give more accurate advice. JMHO aloha

Thank you for your answer

m,

Ooops, I meant to say only run the irrigation system when the tank is full. The other ways is to run your pump from your controller only and fill the tank the run your irrigation after with another program that doesn't run the pump. Aloha