The very specific initial terms for high-level Japanese delegates to fly to a US base on Iejima, near Okinawa to transfer to Manila in a US plane to discuss surrender terms were set out by MacArthur in two broadcasts on 15th August 1945:

At 0930 hours:

I have been designated as the Supreme Commander for the Allied Powers, the United States, the Republic of China, the United Kingdom, and the Union of Soviet Socialist Republics, and empowered to arrange directly with the Japanese authorities for the cessation of hostilities at the earliest practicable date.

It is desired that a radio station in the Tokyo area be officially designated for continuous use in handling radio communications between this headquarters and your headquarters. Your reply to this message should give all signs, frequencies, and station designations.

It is desired that the radio communications with my headquarters in Manila be handled in English text. Pending designation by you of a station in the Tokyo area for use as above indicated, stations JUM, repeat JUM, on frequency 13,705, repeat 13,705, kilocycles, will be used for this purpose; and WTA, repeat WTA, Manila, will reply on 15,965, repeat 15,965, kilocycles.

Upon receipt of this message acknowledge. MACARTHUR

At 0952 hours:

Pursuant to the acceptance of the terms of surrender of the Allied Powers by the Emperor of Japan, the Japanese Imperial Government, and the Japanese Imperial Headquarters, the Supreme Commander for the Allied Powers hereby directs the immediate cessation of hostilities by the Japanese forces. The Supreme Commander for the Allied Powers is to be notified at once of the effective date and hour of such cessation of hostilities, whereupon the Allied forces will be directed to cease hostilities.

The Supreme Commander of the Allied Powers further directs the Japanese Imperial Government to send to his headquarters at Manila, Philippine Islands, a competent representative empowered to receive in the name of the Emperor of Japan, the Japanese Imperial Government, and the Japanese Imperial General Headquarters certain requirements for carrying into effect the terms of surrender. The above representative will present to the Supreme Commander for the Allied Powers upon his arrival a document authenticated by the Emperor of Japan, empowering him to receive the requirements of the Supreme Commander for the Allied Powers.

The representative will be accompanied by competent advisers representing the Japanese Army, the Japanese Navy, and Japanese Air Forces. The latter adviser will be one thoroughly familiar with airdrome facilities in the Tokyo area.

Procedure for transport of the above party under safe-conduct is prescribed as follows: The party will travel in a Japanese airplane to an airdrome on the island of Ie Shima, from which point they will be transported to Manila, Philippine Islands, in a United States airplane. They will be returned to Japan in the same manner. The party will employ an unarmed airplane, type Zero, model 22, L2, D3.

Such airplane will be painted all white and will bear upon the side of its fuselage and the top and bottom of each wing green crosses easily recognizable at 500 yards. The airplane will be capable of in-flight voice communications, in English, on a frequency of 6,970 kilocycles.

The airplane will proceed to an airdrome on the island of Ie Shima, identified by two white crosses prominently displayed in the center of the runway. The exact date and hour this airplane will depart from Sata Misaki, on the southern tip of Kyushu, the route and altitude of the flight, and estimated time of arrival in Ie Shima will be broadcast six hours in advance, in English, from Tokyo on a frequency of 16,125 kilocycles. Acknowledgment by radio from this headquarters of the receipt of such broadcast is required prior to take-off of the airplane. Weather permitting, the airplane will depart from Sata Misaki between the hours of 0800 and 1100 Tokyo time on the seventeenth day of August 1945. In communications regarding this flight, the code designation “Bataan” will be employed.

The airplane will approach Ie Shima on able course of 180 degrees and circle landing field at 1,000 feet or below the cloud layer until joined by an escort of United States Army P-38’s which will lead it to able landing. Such escort may join the airplane prior to arrival at Ie Shima. MACARTHUR

The green cross markings on a white background became the de facto markings for aircraft negotiating local surrenders by the Japanese all over the Pacific. Given the scarcity of supplies and time constraints all over white paint was not always possible. The important point was that the Hinomaru (the red Rising Sun roundel) was covered by a green cross on a white background. I don't know if the cross was chosen to obliterate the Hinomaru as a deliberate humiliation or simply because a green cross was the direct visual opposite of a red disc, but the fact that MacArthur chose "Bataan" as the call sign shows some possible intent.

Either way it was an effective and widely used signal that a plane was engaged in surrender related activities and was not to be attacked.

If you can put up with/ignore the purple prose there is a fascinating collection of "Green Cross" photographs here.

Edit: typos

I can't seem to find specific details about the technical part, but given that the Japanese government ordered Japanese forces to co-operate with the Allies after the surrender, likely through contacts or liaisons between Japanese and Allied forces between the acceptance of surrender and the official Instrument of Surrender on 2 September 1945.

After the official surrender Japanese forces were ordered to comply and co-operate with Allied directives, SCAP General Order No.1 directed Imperial General Headquarters to surrender to specified Allied formations depending on their location, so this again would likely involve contact or liaisons to organise Allied forces ability to utilise facilities.