The correct sequence (Option 1) of the events includes the following:

I. The August Offer: The first event was the August Offer that was proposed by Lord Linlithgow in August 1940. It was the first time that the British government officially recognized the Indian independence movement and made an offer aimed at securing Indian cooperation during the World War II.

III. The Quit India Movement: Following the August Offer, the Quit India Movement was launched by the Indian National Congress in August 1942, demanding an end to British Rule in India.

II. The INA Trials: Post the Quit India Movement, the Indian National Army (INA) trials took place (1945-1946). Soldiers of the INA were trialed in India by the British colonial authorities for treason.

IV. The Royal Indian Naval Ratings` Revolt: Lastly, the Royal Indian Naval Ratings` Revolt was a rebellion by Indian sailors of the Royal Indian Navy on board ship and shore establishments at Mumbai harbour in February 1946.

Options 2, 3, and 4 are incorrect because they do not correctly represent the chronological order of these events.