OP, your car was towed because it was in contravention and according to the council fell within the scope of its policy for removing vehicles in these circumstances. As we understand it, the contravention was being parked without displaying a valid permit or displaying an invalid permit. We'll know when we see the PCNs.
As regards 'Another PCN was still in the windscreen soaking wet and still need to be paid.', IMO no. The authority may not recover further charges after the event, they should have recovered these while you were at the pound:
In the case of a vehicle found in an area that is a civil enforcement area for parking contraventions, the relevant charges are—
(a)any penalty charge payable in respect of the parking of the vehicle in the place from which it was removed,
(b)such unpaid earlier penalty charges relating to the vehicle as may be prescribed, and
(c)such sums in respect of the removal and storage of the vehicle—
(i)as the authority may require in accordance with Schedule 9 of the Traffic Management Act 2004
Which PCN was paid, the earlier or the later(in terms of their dates of contravention)?