We have come to learn that it is common practice for banks to open a new tab after the user's authentication, mainly on iOS devices. This is not something TrueLayer can control as it's managed by the OS and the bank app.
However, if you have cookie settings that must apply on the new tab, - the one that is triggered after the user has authenticated in the bank app/website- please take into account that cookies can be read in the new tab as can local storage.
Therefore, make sure your data is stored on local storage as only local storage is accessible across tabs, not session storage.