safari > Preferences > Privacy
Once I have logged into my small local bank's web site, all I have to do to satisfy MY online banking to pay bills is to uncheck:
[_] Prevent cross site tracking
and CheckFree loads its generic payment window in the banking browser window and all works as expected.
My habit is to leave the Safari Preferences window open, so that I remember to change that setting back before wandering off.
My BIG National bank has figured out how to do this without ANY action on my part -- but they may have written their own special bank-specific "front end" software to display their own special bill pay in their own window, instead of linking to the CheckFree software.
All the checks from all the bill pay sources look the same, and come from Check-Free.