Righty Tighty!

This is from the movie 'The Pearl Harbor'

Here are two pilots, Danny and Rafe, playing chicken with each other.
It was just a joke, but it's gotten serious and they are about to collide any sec. This is part of their conversation.

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Which way you goin'?

I guess I'll go right. No, uh, left. I'll go left.

OK, we're goin' left, right?

Ri--uh, right. Right?

Right like we're goin' right, or right like we're goin' left?

Well, now you got me all mixed up! I don't know. Make up your mind.

God, Rafe, we're going right! Righty-tighty!

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Not having seen the phrase 'Righty-tighty',
I looked up the dictionary to realize it's about tightening bolts or nuts.

Now, at the last scene, Danny cried out 'Righty tighty'
and I wonder if I should turn to left or right if I get to hear 'Righty tighty'.

When I'm told 'Righty tighty!', should I turn to right or left?
I guess this might be very helpful 'cause it might save my life.

Here's the video.

https://www.youtube.com/watch?v=9YSzAawigiI