Okay, one more time...
The autoflowering trait is a recessive trait, the photoperiod trait is dominant. We represent this as P for photoperiod and p for autoflower. When we cross two plants, they will each contribute one geen. In order for a plant to show the autoflowering trait, it must have both recessive genes pp, any other combination, PP, Pp, pP, will be a photoperiod. We can get a rough idea of the contribution using a punnett square. So in your example, when we cross an autoflower (pp) with a photoperiod (PP) the F1 generation will be all photoperiod.
F1 - Autoflower (pp) x Photoperiod (PP)
If you cross two plants from the F1 generation (Pp) then you will have 25% autoflowers (pp). Some people refer to these as "Fast" versions.
F2 - Photoperiod (Pp) x Photoperiod (Pp)
If instead in you crossed a plant from the F1 generation (Pp) with the saved autoflower pollen (pp) then you will have 50% autoflowers. They will also be more similar to the original autoflower, and this would be referred to as a back cross.
F2 - Photoperiod (Pp) x Autoflower (pp)
However you do it, to maintain 100% autoflower (pp), you always have to cross two autoflowers (pp) together.
F3 - Autoflower (pp) x Autoflower (pp)