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Credit appears on the billing statement for the month the fee/charge hit. It is not an instantaneous credit that you'll see in the account online, it only applies at close of statement.

The year your purchase counts against is based on the statement date, not date of purchase. Tickets purchased late in the year, especially in December, will almost certainly count against the benefit in the following calendar year. Do not wait until the end of the calendar year to use your credits!

Summary of reimbursement options by airline

Please edit the wikipost to add your specific knowledge of airlines.

Aer Lingus: Tickets work
Air Asia: Tickets worked booked on airline site.
Air Canada: Tickets (via travel agent) work. Bag fees work
Air France: Award fees work
Alaska Airlines: Tickets work. In-flight food does not. Gift certificates do not.
Allegiant: Tickets work, with effort.
Atlantic Airways: Tickets work.
American Airlines: Gift certificates work. Status challenge payment works. In-flight food works. Tickets Work Baggage Fees at Airport works.
ANA: Award taxes
Avianca: Upgrade fees work.
British Airways: Tickets work.
Cebu Pacific: Tickets and bag fees work.
China Airlines: Tickets work.
Delta: Bag fees work. Tickets work. Gift cards work.
Emirates: Gift shop purchases work.
Etihad: Award taxes/fees work
EVA: Sky Shop
Frontier: Ticketing online works 6/18/17
Hawaiian: Bag fees work.
JetBlue: Bag fees work. Tickets work.
KLM: Tickets work.
Korean Air: Ticket (via travel agent) works.
Lufthansa: Tickets work.
Malaysia Airlines: Tickets Work
Qatar Airways: Tickets work.
Turkish Airlines: Tickets work. Upgrade fees work.
Southwest: Gift certificates work. Award fees work. In-flight meal purchases do not work.
Sun Country: Tickets work.
Thomas Cook Airlines: flight from UK to USA, priced in GBP, worked
United: Gift certificates work. Tickets work.
Virgin Atlantic: taxes+YQ for award ticket worked
Points + Cash booking via TY portal: Yes, after manual request.