The general approach is to implement deadbanding.
A deadband (sometimes called a neutral zone) is an area of a signal
range or band where no action occurs (the system is dead). Deadband is
used in voltage regulators and other controllers. The purpose is
common, to prevent oscillation or repeated activation-deactivation
cycles (called 'hunting' in proportional control systems).
You may also be dealing with hysteresis.
Hysteresis is the dependence of a system not only on its current
environment but also on its past environment. This dependence arises
because the system can be in more than one internal state. To predict
its future development, either its internal state or its history must
be known.1 If a given input alternately increases and decreases, the
output tends to form a loop
In layman's terms you can think of hysteresis as overshoot. In other words when one turns on a heater and then turns it off at a certain temperature the temperature may continue to rise somewhat even after the heater is turned off. Of course a PID controller should handle this, but you have two independent controllers which may be battling each other.