The magnet moves as shown.The field of the magnet through the coil is
The diagram represent the current in the coil due to the induced field.
When the magnetic south pole enters in the coil the field are cut form the outside - left and the to oppose
this change an inward right magnetic field is produced. According to thumbs rule , the direction of the current is along the thumb when field is inward and right. This causes induced current in the coil flowing from right to left in the wounded coil (highlighted in blue).