Yes, ... the poles are opposing indeed. They have to, otherwise there is no current induced in the coil. It has to do with the famous right hand rule. I'll try to explain it. The coil sits in the middle on the rotating donut. On the right and on the left sits a magnet. The coil is now getting hit with a field from the right and from the left.
A coils "right side" which gets hit with a North field from the right will experience a current in the "up" direction.
A coils "left side" which gets hit with a North field from the left will experience a current in the "down" direction.
If you do a North South, then you will see that the currents might go on both sides Up, Up or down, down, ...therefore no circulation.

I hope I used the right hand rule in the correct manner, (might have switched the Ups and downs)if not then I'll apologize, but the principle described above is a good way of showing what goes on in the toroid.
Hope that helps, let me know if you need more infos.
Powerbuoy