score:6
From the Air Astana website:
Transit visas are not required for those transiting through the same terminal, but necessary for those transferring to another terminal if no transfer zone is provided. Transit visas are issued upon provision of a visa valid to enter the country of destination and relevant tickets with confirmation of departure date from the transfer point on the territory of Kazakhstan, no later than 5 days from the moment of arrival to the port or station in Kazakhstan.
This could be read in such a way that indicates you will be issued a visa on arrival, but it also doesn't actually state that. Further down the page:
- Application for an entry visa should be made to the Kazakhstan diplomatic or consular office in the country of your residence. You can find a list of all Kazakhstan diplomatic offices in the Travel Information/Diplomatic Missions section of this website.
That, to me, is pretty clear - Air Astana says you should apply for an entry visa in advance.
The Kazakhstan embassy website also has no mention of a transit visa being issuable on arrival, it simply has a form for you to apply in advance.
Indian citizens are not a visa-free traveller to Kazakhstan, while other countries do enjoy visa-free entry - this may complicate matters and it may have been confused for a transit visa in some cases.
Other websites suggest that Indian citizens need to obtain a transit visa in advance:
A valid passport and visa are required to transit through Kazakhstan.
I would suggest that in this case, Timatic is not accurate and the situation with regard to transit visas on arrival into Kazakhstan isn't as clear cut as it might otherwise be.
Given that even caravanistan.com suggests that you need a correctly sized passport photo and letter of invitation even for a transit visa, that to me suggests that visa-on-arrival is probably not accurate given that most people won't be carrying either of those around with them randomly...
In answer to the actual question asked, and not the underlying situation...
You write a letter of complaint to the Department for Visas and Registration under the Ministry of Internal Affairs and inform them what happened.
Don't expect any compensation or even a response however...
In a comment, the question asker asked about the costs of flying the inadmissible person out of the country
Under ICAO rules, updated in 2015, the aircraft operator can recover costs involved in the transportation:
5.10 When a person is found inadmissible and is returned to the aircraft operator for transport away from the territory of the State, the aircraft operator shall not be precluded from recovering from such person any transportation costs involved in his removal.
What that actually boils down to is up to the lawyers - can the airline charge you the most expensive ticket for the seat you occupy? That is currently untested law.