Students are not, per se, exempt from paying Council Tax. It's simply that a building solely occupied by students becomes exempt.
Unlike the old Community Charge (or Poll Tax as it was more commonly known), Council Tax is payable in respect of a building not by individual people. If, say, the property was leased in the name of one of the employed people, it would be perfectly reasonable for that person to expect all the other people, joining in the house-share arrangements, to each contribute one sixth of the Council Tax. (Indeed, if this was not so, many students would find it extremely difficult to find accommodation. Leaseholders would not want to accept students to join in the house-share if their presence meant increased bills for others in the house).
This is one of the things which should have really been sorted out before the people agreed on the house-share arrangement but, in the absence of any such agreement, it seems reasonable that everyone should contribute to the Council Tax.
Chris