From the point where Ciri fled Cintra to the point when she arrives at Thanedd, nobody knows where she was and was likely assumed dead. Geralt did take various measures to hide her away, including the whole "fake Ciri" plot.
As for Emhyr, his deal with Vilgefortz goes way back to before Emhyr became Emperor (spoiler, not really relevant to the question):
From the point when Ciri was born, pretty much. Duny and Vilgefortz schemed to fake the death of Duny, Pavetta and Ciri and go to Nilfgaard. The plot failed as Pavetta learnt of it, though Pavetta herself died.
Emhyr didn't "hire" Vilgefortz but rather each of them thought they could manipulate the other to achieve their personal goals.
In the books Emhyr and Vilgefortz actually launch somewhat parallel search parties. First there is Cahir and Rience - their search efforts didn't really have any success until Ciri surfaced of her own will before the Brotherhood. And after the Thanedd coup, Rience had no success at all in finding her.
Whereas Emhyr's search party later on through Stefan Skellen and Leo Bonhart actually did manage to track Ciri down. Skellen indirectly having access to the whole extensive Nilfgaard intelligence network and Ciri was also in Nilfgaard at the time.
At the same time, Geralt, Yennefer and the Lodge of Sorceresses were all also looking for Ciri by using their various networks - unsuccessfully.
Conclusion: Ciri wasn't all that easy to find.
Notably, all searches for Ciri relied on intelligence, not magic. Vilgefortz himself didn't actively take part in the searches.
Avallac'h didn't have any such resources or intelligence networks. He only relied on prophecies and that Ciri was destined to find the Tower of the Swallow eventually, which proved to be true. What he could see/not see isn't made clear, since what magic can/can't do isn't all that well-defined in the books.
Also the Aen Elle couldn't initially know that Ciri had inherited the powers of the Elder Blood, since these don't manifest with every generation. Ciri's grandmother Calanthe was the first of the reunited Lara Dorren blood lines but the various abilities never manifested themselves in her. It was only during the Thanedd events that they learnt that Ciri had such abilities. If they had known earlier, then maybe the Wild Hunt would have made an attempt to track her down.
(At one point earlier Ciri enters a trance and speaks with someone in a dream, but it's not really clear who this was. Could have been Vilgefortz, Avallac'h or maybe Eredin even.)
