Playing some clown on cockatrice. He had a {heartless sumuning} deck he had 2 {solem simulacrum} with a {wurmcoil engine}. I hard cast {devastation tide} then on his turn I {think twice} and miracle {temporal mastery}. He was like well you cast it on my turn so u only get a regular turn after this one. I was like read the card. He was like I did. I ended up hard casting a {temporal mastery} then {entreat the angels} four 6 4/4 angels. I am sure I played it right but how do u argue with guys that won't belive you? Thanks.
Temporal Mastery is very simple: take an extra turn after this one. The key word is EXTRA. Extra means 1 more than you would normally have. So if you played it on your opponent's turn, you would get one turn more than what you would normally have after his turn ends. You are correct; Temporal Mastery ({Time Walk}) will give you an extra turn no matter who's turn you play it on and no matter how many extra turns you have already had.
Think of doing the same thing in a three player game. You would take a turn after his turn, but before the third players turn. So instead of A-B-C, it would be A-B-A-C. (you being A of course;))