Driving a linear actuator from a home automation system
I believe this circuit will work as you intended. It took me a minute to decipher your use of S1 and S2 to represent the two power signals from the home automation system. It's not totally clear, but I think I understand what you meant. I'm also assuming that the relays you've chosen are appropriately sized since you didn't specify any part numbers.

I'd add a few circuit protection elements for safety and to prolong the life of the system.

Mainly, a fuse in series with the power brick. This is a fairly high-wattage motor. If it stalls on something or shorts internally, you'll have a lot of energy pumping into the system until you notice the fault - which may not happen until you start smelling the smoke.

A large, fast switching diode across each relay may be a good idea as well. When the contactor suddenly separates - but before it makes contact with the + side of the power supply - the inductance of the motor will spike the voltage looking for a path for the current. It may cause an arc to form from the contactor to one of the other terminals of the relay. The arcing could damage the relay over time. A diode would give a path for the current to flow back into the power supply for that split second before the contactor is finished moving. The anode of the diode would be connected to the motor side of each relay and the cathode to the pin connected to the positive side of the power supply.