If the funfair staff are correct and they never asked about Tia and were never there, then what happened during that time between 7.15 and the roughly 21.40 that SH and CS were supposed to be searching for her.
And this is the perplexing bit, because as
he/they set the timeline, not the police, not the public -- there was no need for it
Unless we're missing a planet-sized piece of the puzzle, no-one could have seen Tia anywhere because she never did set off for the shops - so there was no need to 'fill in' chunks of time in order to 'fit' anyone else's version of events
Not as if there had been a definite sighting of Tia on CCTV or by any witness (as far as we know) which required them to conform with any particular time-line
The killer was therefore free to invent the entire day/afternoon. As I said earlier, his story would have been just as believable if he'd claimed CS came home and went to sleep (23 hour shift) and he conked out on the sofa with both of them only awakening at 6, 7, 8 -- take your pick
There was no need to raise the alarm or notify the police at any particular time because no-one at that point (far as we know) knew she was supposedly missing. So why did they and why the mysterious inclusion of a subsequently and strongly denied search of a fair ?
The only thing I can think of right now is that the killer/s feared he/they had been seen driving somewhere at roughly the same time the alleged 'following the bus' and 'fun fair search' supposedly occurred
If they'd been dumping the body at around that time, I could understand why he/they may have attempted to cover that by claiming they were driving 'round following buses and searching fair
However, as the body seems to have remained in the loft the entire week, that's ruled out of the equation. Unless the body in the loft is not Tia and they did dump Tia's body sometime on Friday late afternoon, after which they attempted to cover their tracks by including the bus-chase and fun-fair