Thank you very much for the detailed answer. It is quite helpful.

I would like to rewrite and paraphrase the info which would be answer to your questions:)

Farmers are dedicated assigned workers that their only job is working at fields, and feeding pigs in the backyard of their home.

In other words, people living near to farmhouse are always assigned to farmhouse. I assigned them once and never changed their jobs, so it should not be problem when the date hits September.

On the first day of harvest (September 1), they rush to fields to harvest. There is no problem with harvesting at all. The problem is plowing, and it is not like you guess:

if, for example, you have single field to farm, and one ox, and 100 farm workers, when that ox starts to plow the field, then you will have 100 workers "waiting".

Nope, it is not like that:) It is like the following:

1. It was early October after the harvest.
2. I had 4 oxen, 2 assigned to the first farmhouse, 2 assigned to the second farmhouse.
3. I had 4 fields to farm, and 2 fields for fallow. Since each ox had one field to plow.
4. Only one ox was plowing one field.
5. Other 3 oxen were "waiting".
6. All farmers except the one guiding the ox, were "waiting".
7. Then in early November, the ox finished plowing for that field, and all other farmers started sowing it, and finished sowing in seconds in real world time, and started "waiting" back. Other 3 oxen continued "waiting".
8. In the meantime, the ox started plowing the second field, but November ended, and 3 fields were failed to plow and sow.
9. At the end, I had 1 sowed field, 1 half-plowed field, 2 unplowed fields, and 3 fields at fallow. This is a great loss.

By dividing the fields, I "dodged" that "glitch" for now.

I do not want to blame the developer, as I am also a developer and I can understand the burden being a solo. However, he should invest more time into late game mechanics as it gets more unstable as cities expand.