I agree with Jraef, of course.
Let's say the rotating magnetic field is a ring of permanent magnet poles [N-S]. Let's say these poles do not rotate but only rotor is rotating with the difference of velocities. That means it rotates backward [counter clock wise] with the speed of v=slip*2*pi()*f/p*Rgap [Rgap=radius of the gap; p=number of pole pairs].
When a rotor bar of speed v passes a pole of B field an emf is produced E=B*leng of bar*v and since there are 2p poles [p pair of N-S] an emf wave will rotate with v velocity of the rotor.
A current will circulate through the bar but the current wave is delayed with the impedance angle and will produce a connected with rotor field wave.
This field wave rotates with the f*(1-s)*60/p rpm.
Since each rotor bar will pass the same pole at different time a different angle has to be applied for each current in each bar. You may consider then [if you want it] each bar as another phase [or not]. However, as you could see, no 3 phases are involved here but only number of poles. Of course, we give balanced 3 phase current (distributed in time) to balanced 3 phase winding (distributed in space) to produce the stator field.