Matching Transactions / Auto Entry / 2 Checking Accounts

Old user, new file. I am new to auto-entry. I am not sure if that's part of my problem.
Two checking accounts: [Bank 1] and [Bank 2].
Transfers TO [Bank 2] always come from [Bank 1].
There are no transfers FROM Bank 2 to Bank 1.
On initial download, all transfers from Bank 1 to Bank 2 are assigned [Bank 2] category in Bank 2's registry.
The same transactions were downloaded to Bank 1 with the category of [Bank 1].
IOTW, the downloads are being assigned the category of their account name.
Goal: Change the category in Bank 2 to [Bank 1] for transfers IN.
If I change the category in Bank 2's register, it shows up in Bank 1 as a duplicate payment.
What is the fix, and is this a side-effect of auto-entry?
Answers
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Amplification: All transfers are recorded back to the account in their register.
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