There are 6 possible ways / modes / types each rotator can permute its triangles. 

The game has a specific tutorial in the game to play with each rotationtype !
Here is an overview :

1. Vinyl Record Type : The simplest rotation, where all triangles keep their orientation towards the rotator. Just like sitting on a vinyl record.
   
   
2.  Spin Forward : The triangle is given an extra push on the tip facing the rotator (the center- tip) into the same direction as the rotation itself. 
   In itself it will actually rotate 120° into the opposite direction of the combined rotation. Visualize this with a left or right hand rule.
   
   
3.  Spin Backward : The opposite of the above. You can imagine the triangle being held back at the center-tip. I.e. it will rotator around itself by 120° in the same direction as the main rotation.
   
   
4. Center Axis Flip : Is the same as Type 1 plus the triangle flips over and changes face up & down.
   Visually the triangles flip over the symmetry axis to their next spot.
   
   
5. Clockwise conserved : Imagine an axis from every triangle to its clockwise facing corner. The triangle is flipped over this axis, and all triangles pointing along that axis keep that orientation.
   It's a combination of type 4 and 3.
   
   
6. Counter-Clockwise Flip : ... as you may have guessed. The same as 5 except counterclockwise. It combines type 4 & 2.

 Since this is all a bit tough to remember, playing with specific puzzles to see and practice each rotation really really helps.
The 'Spin Tutorial' in the game has the right puzzles.

Most puzzles have only one rotationtype, but they can be mixed up too.
If they are mixed, every rotation-type uses a specific color, as shown on the lower left corner (RTypeIndicator).