I breed my own autos. I have stabilized 3 photo x auto crosses into autoflowering strains. They follow mendalian punett square recessive trait passing.
So... the first auto/photo cross will most likely (99.6%) be all photo with a recessive auto gene cared in all progeny. The auto trait shows in the F2 progeny at about 25%. Successive auto x auto sibling crossing will produce a higher percentage of he recessive auto trait.
1st cross = 0% auto
2nd cross = 25% auto
3rd cross = 86% auto
4th cross = 96% auto
..... and so on...
I've stopped at F4 progeny for testing on one strain and have had 100% autos reported back from growers with 3-4 phenotypes mainly showing up.
If you want stability in ur new strain you must selectively cross alike phenotypes at least 6-7 times. This will get the phenotypic expression down to 1-2 or about 90% of plants with the same traits.
To answer your original question, according your graphic, the F1 of both crosses will carry the auto gene and none will be auto plants. Once you cross the F1s it will start to show from recombination but only when it's a double recessive pass from the F1s i.e. a very low percentage. Most likely around 12.6% since you are using 2 photo/auto F1s to start. I have not done this because of the time required and the plant count required to see the 12% on the first F2 planting. I have planted 50 seeds and not seen an auto at this stage and shelfed the project.
I would suggest working each photo/auto cross separately up to the F4 progeny. Then when they start to become auto stable cross the separate lines to make your (SUPER AUTO!!!). This will bring all avaliable phenos from the original crosses together in an auto format so you can start pheno hunting and backcrossing to lock in the traits and or phenotypes you want. Simple
caution
this takes alot.... of time to do correctly.
For home grown autos you can stop as soon as F4 and run the S!@# out of them with good results and tell people that you made it yourself. You can do this in 1 year if you're good and you plant as soon as the seeds are finished.
There are always ways of cheating but not recommended ( as in feminized, sibling crossing or selfing one pheno to isolate the auto gene). These will degrade the line quickly.
The best out come I've had for "fun/personal" stash seeds is to buy 3-5 auto strains with different lineage (the parents). They will be all Feminized seeds probably so you will need to get good at feminizing. Start 2 strains. Soon as you can clone one strain (or both) for feminized pollen donors. Start STS spary evey 3 days ss soon as you clone them. They will flip and produce pollen in about 20 days just in time to pollinate the other strain.
F1 created......
Germinate a seed from the F1 batch and another of your "parent" seeds. Repeat this process by using the parent as the pollen doner on your F1 cross. The progeny will be a 3 way F1 cross. Keep going until you have "breed " all your parent lines into the now 5 way F1 you have. This is where the magic comes in.
Grow 25 of the 5way F1 seeds and select the best 2 totally different phenos. Breed these 2 plants together and look for the winners. If you keep selecting alike phenos it will become stable after several crosses.
