AMTS excludes the standard 90-minute AMT ticket, day tickets, FCE metro tickets and ordinary season passes from the Alibus. The €4.00 airport ticket is its own product and has to be bought separately — though the other way round works, because the €4.00 ticket then covers 90 minutes of ordinary city buses.
The railway station of that name is about 600 m from the terminal, linked by the AMTS 524S shuttle (every 10 minutes, 04:30–22:40, €1.00). A Trenitalia ticket to 'Catania Aeroporto Fontanarossa' does not include the shuttle; you need the destination 'Catania Aeroporto Fontanarossa Bus', where the bus leg is priced at €1.40.
The last Alibus leaves the airport at 00:30 and the first is at 04:40, and the airport railway shuttle stops at 22:40. The overnight 524S runs about every 15 minutes, but only between the terminal, the railway station and the park-and-ride — it does not go into Catania.
Catania's 'Taxi by Night' flat fare of €12, from 20:00 to 05:00 for up to four passengers, applies inside the historic centre only. It is not an airport fare: the airport route has its own fixed €27 price. A driver quoting €12 for a 23:00 run into town is selling you the wrong tariff.
The airport warns that any vehicle waiting outside the marked areas may be driven by someone without a regular licence and can charge more than the Comune di Catania tariff. Complaints go to trasporto.pubblico@comune.catania.it with the CP Taxi licence number shown on the car, and the airport's radio-taxi line is +39 095 330966.