I transferred a Dropbox API app from one account to another account via submitting a ticket to Dropbox support, they said app is transferred and they are right I see app in my new account, but the problem is uploading to the app sends files to old account, not new one! I am using generated access tokens from old account to upload to my own account, and as Dropbox agent says generated access tokens from previous account are still active.
That's correct, this is the expected behavior.
Transferring ownership of a Dropbox API app changes who "owns" and can configure the API app itself, but it does not affect the existing access tokens for that app.
A Dropbox API access token identifies a particular app-user pair, and allows access to that account to the extent allowed by the permission registered to the API app.
Any number of access tokens for a particular Dropbox API app can be created for any number of users. Whether a particular access token was created via the "Generate" button on the App Console on the current owner's account, or via the normal OAuth app authorization flow, it won't be affected by transferring ownership of the app itself.
If you need an access token for the new owner of the app, you can use either method to get one. This will be different from the access token for the old owner.