Bank account not in the Trust & must go through probate, any advice ?

Hello,

My dad had a Bank account that my sister had the ability to write checks from. She said the bank called it a power of attorney (POA) account.

The money came from a CD at the same bank that was in the trust and titled as such. The money was transferred from the CD to this "POA account" which was just a checking account.

At that time the bank said it could not be in the trust as it was a POA account but would transfer at death into the trust.

My father passed away and now they say it must go through probate as it is not in the trust and it is over the pour over will amount in CA.

My sister said she had the same setup on another account at another bank and they said it would transfer to the trust at death. It looks like that has happened according to the bank so far.

Questions:

1. Is there anything we can do to avoid probate still ?

2. Do banks have different policies on these POA accounts ?

3. Anything else to think about ?