It's called a DEILD, dream exit induced lucid dream. You stay perfectly still after you wake up and then you imagine a dream and you can step into it. I did it once, it's easiest with the dream you just exited but it can work for new dreams as well if you have skills.
No, I don't think that's what he's talking about.
DEILD requires you to wake up after one dream to enter another one. I'm pretty sure the OP is saying he went out of one dream in the beginning of the night and then between his 2nd nad 1st REM periods he went straight into the next dream instead of two separate dreams.
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