As expected. You are dealing with feckwit morons at Tusker. You should write to them and inform them that they have misinterpreted the law when they say:
For Private Parking notifications only (Parking Charge Notice), please see the additional information below.
The legislation has changed. To read more about this within The Protection of Freedoms Act 2012, please log onto http://www.legislation.gov.uk/ukpga/2012/9/schedule/4/enacted.
The changes mean that Tuskerdirect Limited as the registered keeper can be held liable for these charges if you take no action.
In the event we receive a second notification from a Private Parking Operator for the same offence, we will pay the outstanding amount and recharge this amount to you. Please note this additional step may incur a further administration fee as set out in the terms and conditions of your contract.
Point out that as long as they have transferred liability as per paragraph 13 of PoFA, they can no longer be liable for the charge and their suggestion that they could still be held liable for the charge if you, the Hirer, take no action, is mendacious and not possible under the Act.
Therefore, they have misrepresented the law when they included that bit in their letter.
Anyway, the important bit for you to take note of now is this piece in their letter:
We have given your details to the relevant authority transferring liability of this offence to you. The authority will now contact you directly.
Again, ignoring the fact that they have used the terms "authority" and "offence", which shows an utter lack of competence within their team, you now have to wait until you receive an NtH in your name before you can do anything else.
For now, write to them and point out their ignorance of the law in relation to their liability if they have complied with paragraph 13 of PoFA.