Is this dream recall pattern normal?

Lately I only remember having dreams once I wake up and fall back asleep.

An example would be when I went to sleep yesterday.. Got in bed late, around 1, and actually fell asleep around 2 since I had a lot on my mind. Woke up around 7 or 6 and didn't remember anything. I then went to sleep and remember having 2 very vivid dreams when I woke up.

I heard something about not actually going into REM or dreaming until 4-6 hours into sleep from I think the Paradiso rules or something?

Ya it's normal probally were just to tired to remember.