Hmmm. Im not familiar with that specific app, but I do know that most bank apps are web versions of the desktop site. Can you use the phone browser to access the www ATFCU com site? Are they comparable in function? Does the mobile site have a log out button?
Make a phone call from another phone to the Austin Telco Federal Credit Union and ask to be connected with their "IT person" the tech that designs their web page and have that person walk you into the correct browser and setup for you mobile device.
You are smart to be vigilant here.
First, try Settings | Display then scroll down to Advanced Settings Front Touch buttons, and choose an option that puts the menu (three horizontal lines) on the display. Maybe the program will respond to the menu button and allow you to set it to auto-log out...
For my Credit Union app, the front buttons (with menu) always appear at the bottom of the screen.
This is VERY SERIOUS for a banking app.
Also try your back button. The program should ask you if you wish to log-out (which the program should be written to support that). Also, the program should be written to support auto-logout after so many minutes of inactivity. If it does neither, you NEED to talk to the IT team, or a manager at the bank responsible for mobile banking and the contractors writing the app, because that situation doesn't seem like a phone-specific vulnerability and it's a very very bad thing to leave a banking app logged in (even if that can be turned off with the menu button, it should not be a default).
Let them know you are an informed consumer. They need to be much more sophisticated in the mobile banking realm if they truly have these app vulnerabilities.