As mentioned in the comments of the question, the function in question is normally performed by a control mixing unit (see this related question), also called control mixing or controller mixing. The principle is quite simple. Given the three actuators of your swashplate, you have to "map" the control inputs from the pilot's stick (so roll, pitch and collective inputs) to the three actuators given in your picture, such that the swashplate tilts or translates as requested.
Three examples:
The simples case is, when the pilot pulls on his collective, then all three actuators have to move down.
When the pilot gives a roll-right-input the desired output is that the swashplate tilts backward (seen in direction of flight). Therefore, in your diagramm actuator 1 has to move up, and actuator 2 and 3 have to move down a bit.
When the pilot gives a pitch-forward-input, the desired output is that the swashplate tilts to the left (seen in direction of flight). Therefore, in your diagramm actuator 1 stays constant, actuator 2 moves up a bit and actuator 2 moves down a bit.
Additionally such a mixing unit also automatically mixes inputs for example by automatically applying a rudder input whenever the collective is pulled.
It seems to me, that you textbook differentiates between these two actions. Mixing (e.g. automatically applying yaw when collective is pulled) is defined as mixing, and "phasing" is the act of distributing the mixed inputs to the servos spaced 60° apart.
As a reference look at this diagram of the control linkages of a Sikorsky S76, and observer that the mixing is performed in the same step as the "phasing".
Personally I have never heard of this, although I am involved in computerized helicopter control quite a bit. I would put such a function under "mixing". My opinion is that normally one does not differentiate between these two parts.
