You must rest a compressor until the refrigerant has time to equalize. 3 minutes seems too fast.
Can we assume that you can only control with the units ?
turning them off is simple enough, turning them on is the problem.
you did not mention the heat load in the room.
people ? lights ? other ?
if you can monitor the load in the room, you can predict when you need cooling.
but trying to maintain 1 deg C is hard with good controls.
turn one on, run, turn the second on, run,
when needed alternate which one is on.
as you get too cold, turn of #1
as you get too warm, turn #1 back on. based on your times, this should not be under 15 minutes ?
then, when it gets too cold, turn off #2....
you did not mention how you turn them on an off. normally, a motor starter is used. often has a control coil that has low current. but it may be line voltage. you can control the signal to that coil with a relay that the Arduino can control.
If you have a large budget, there are ways to control very precisely.