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The global governing body had also previously informed the ECB any footage shot in the PMOA must not carry audio or be released before the conclusion of a match.
Speaking at the close of the fourth day, Stokes explained why the public announcement was made during play, detailing it was a plan between his agents and the ECB.
"I just said, 'You guys work with Michael Lumb and Neil Fairbrother, who work with me, and you guys just come up with a plan'," said the all-rounder.
Stokes was in the middle of a bowling spell at the time of the announcement and, with his first delivery after news of his retirement spread, took the wicket of New Zealand's Zak Foulkes.
The Test, and Stokes' international career, did not end until the following day.
The ICC adopted what it described as "minimum standards" for the PMOA in order to support its anti-corruption code.
Neither the ECB nor the ICC have commented. The letter from the ICC was sent the day before the Women's T20 World Cup final at Lord's, when ECB chair Richard Thompson met with Jay Shah, chairman of world cricket's governing body. The ECB has yet to respond to the ICC.
Stokes' retirement has left England looking for a new Test captain in time for the three-match series against Pakistan in August.
Vice-captain Harry Brook has said it would be an "honour" to succeed him, but England are understood to be taking time over an appointment.
A factor in the decision could be uncertainty over the futures of other figures in the England management after a run of poor results in Test cricket and a string of off-field controversies.
Head coach Brendon McCullum and director of cricket Rob Key were both backed in the spring following a review into the Ashes series, which England lost 4-1.
The ECB are now reflecting on the situation around the men's team, but may wait until the conclusion of the ongoing white-ball series against India before making any formal announcements.
Neither Key nor chief executive Richard Gould have spoken publicly since Stokes' retirement.
