The rules for compensation in the UK were set out in the Compensation (Defence) Act 1939. These covered requisitions of land, vessels, vehicles and aircraft, compensation in respect of taking space or accommodation in ships and aircraft and finally, the catch-all
compensation in respect of requisition or acquisition of goods other than vessels, vehicles and aircraft.
The specific rules in regard to compensation in respect of requisition or acquisition of vessels, vehicles and aircraft are set out in part 4 of the Act.
In short, compensation was generally paid from the day that the requisition notice was served until the aircraft was returned, lost or sold. That compensation would be paid at the time when the expenses being compensated for actually incurred.
So, it appears that if the aircraft was being used commercially, the owner would be paid compensation for the loss of earnings. According to section 4(4) of the act, payments would be made at intervals of not less than one month. Presumably this meant they would be made monthly, quarterly, or at some other interval specified in the requisition papers.
If the aircraft were subsequently lost, sold, or destroyed the owner would be compensated for its value at the time of loss (paragraph d). That payment would accrue due at the time of loss, sale or destruction (subsection 5).
In the United States, the legal situation is slightly more complicated. Firstly, under 10 U.S. Code § 2644 - Control of transportation systems in time of war:
In time of war, the President, through the Secretary of Defense, may take possession and assume control of all or part of any system of transportation to transport troops, war material, and equipment, or for other purposes related to the emergency. So far as necessary, he may use the system to the exclusion of other traffic.
This provision was enacted by the 64th Congress in 1916 (Aug. 29, 1916, ch. 418), and remains in force today, so it would have formed the legal basis for any aircraft requisitions during the Second World War.
However, under the Fifth Amendment to the U.S. Constitution,
'private property [shall not] be taken for public use without just compensation'.
From the wording of the relevant section of 10 U.S. Code § 2644, it appears that, unlike the UK, where the government only requisitioned the asset "for the duration", the US government actually assumed ownership of the requisitioned aircraft when the requisition papers were served.
It would appear therefore, that under the Fifth Amendment, compensation would have been payable to the owner of the aircraft immediately.