You probably know where this is heading. See, Mason is more than just some spry convict; he's revealed to be a British Intelligence-trained former SAS captain who was wanted for stealing America's precious secrets. When he was captured, England disavowed all knowledge of his existence and he was put away in Alcatraz in 1962 ... only to escape a year later to presumably take on his true enemy, SPECTRE.
And the harsh mistress of time.
No, seriously -- as others have determined before me, The Rock fits quite well into the James Bond chronology if you also subscribe to the previously discussed theory that the Bond name is actually a code word like 007, which would explain why the character never ages and constantly changes appearance. That means John Mason had taken up the Bond title for Dr. No in 1962, a film that ends with him being taken in by the Coast Guard. He would then have been jailed in Alcatraz for that time and escaped before From Russia With Love and the subsequent adventures -- stopping briefly in America to get some strange (and father an estranged daughter, who we meet in The Rock).
"Related you shay? I best be going."