The ten authorities are mere shareholders, MAG look after the assets on behalf of them However, they will have voted in favour of this move in order for it to go through. Also, Manchester City Council no longer own a controlling stake in MAG, as IFM bought 35% of MAG, with MCC's share reducing to 35%. So effectively STN has been purchased at no cost to the tax payer.
I understand, of course, that the local authorities are not directly running the airports. Nevertheless, as shareholders, they will presumably be receiving dividends, which raises the question of why the users of an airport in Essex should be topping up the coffers of councils in Greater Manchester.
Unless, of course, the profits from STN are simply servicing MAG's debt. In which case what is the point? Empire building??