I agree the policy itself is unclear.
When the regulation is unclear, we have to make some assumption in interpretation.
A common rule is that a law or regulation (a public school policy is a government regulation) is usually prospective (apply for future), not retroactive (apply to past). For example, if a new law makes abortion illegal today, I should not be charged with a crime for abortion I performed yesterday.
For the same reason, if your transfer was after 9/1, the policy applies.
On the other hand, your transfer was 4/1, had the new policy applied to you, your probation would end on 7/1, still before 9/1 regulation effective date. (retroactive) Without the regulation expressly stating the regulation applies retroactively, it's a very hard argument to make.
Had your transfer was 6/2, and 3 month date would be 9/2 and there would be an argument that the new policy might be effective during your NEW probation period and it COULD be applicable (prospective). It's not a strong argument but maybe just close enough in the right court room. In other words, it worths a shot, depend on how you value $4000.
I understand your argument would be that, the policy should apply because it changed six month period to three month period while during your existing probational period, and therefore your probational period would be changed. But think about a person in the same situation as you but terminated on 8/30, one day before 9/1, does his probational period got set to 3 month as well?
We can go down this rabbit hole but I doubt we can come up in some productive outcome. I'd save the $4000 if I were you.
None of above is legal advice. Disclaimer.