I see this when I pay bills and such online, but what isn’t clear to me is whether I should close just this window, close all browser windows, delete temp files and close all windows or… etc.
Their concern is probably with cookies and the “back” button. I would close ALL browser windows to be sure.
My credit union (and some other sites) open the secure areas in a new window. So when you disconnect there is no “back” to go to.
There are two types of cookies, temporary ones stored in the browsers memory, and permanent ones stored on disk. The bill paying site will be setting a temporary cookie that is only deleted when the browser closes. The cookie that remembers your SDMB login is the permanent type and is only cleared when you tell the browser to delete stored cookies.