I'll be honest, I'm not really following the authors logic on this one. I would imagine that the aircraft on a carrier stay on a carrier throughout a deployment (Barring failure related replacements). So when talking about carrier related deployments - squadrons refers to the Manpower rather than the aircraft themselves.
4 squadrons of manpower sounds about right - 1 on board, 1 in Training, 1 on leave and 1 on ramp up. But for the aircraft I cant see you needing more more than 3 - 1 set of the carrier, 1 in maintenance/overhaul, and 1 for Training (probably used by the ramp-up Crew as well).
In Addition, for the Training crew, you can probably achieve the majority of the necessary training in standards F-35A's, the only parts that are different are landing/take-off, but all of your in flight training would be identical. Considering the F-35A is significantly cheaper (to buy and to run) then using them as the majority of your trainers makes considerable sense.
Also, considering the continual squeeze on the MOD's Budget buying F-35A's as your land based squadrons (in combo with the F-35B's as your naval variant) is going to make your maintenance costs significantly lighter - when you only have F-35's as fighters then you can standardise your equipment nicely. Similar to how most Airlines tend to stick with either all Airbus or all Boeing aircraft. it allows your maintenance costs to be cut significantly.
Finally, it sounds like the author is mistaking the RAF with the Fleet Air Arm. The RAF is the land based fleet and you would expect them to upgrade the Tornados to F-35's. The Fleet Air Arm which belongs to the RN controls the aircraft on the carriers, is subservient to the Navy, not to the Air Force. If the Air force is buying F-35A's that doesnt have any effect on what the Navy are purchasing (unless the Air Force purchase is funded by taking money from the Navy). So it really is two separate Topics here...