The Wallet has a priority set at a system level. It will popup over other apps. That’s how it is designed. Apple has no provision for turning it off. But there’s a solution, albeit probably not what you’re hoping for.
All tickets, passes etc. are supposed to be stored in the Wallet app. Tickets, passes and other secure item need to be stored there. The only exception is a third party app.
The app developer needs to add code, that Apple makes available to registered developers, that will suppress Wallet from opening when the third party app is open first.
Download the app the ticket issuer has or use their website and add tickets to Apple Wallet the way intended. If you don’t want to do that, download a third party app and add your tickets there. Hope the developer added the code to the app.
Those are the options that work. Lastly, continue to do what you’re currently doing, but as you noted, that doesn’t work and you might miss your train or plane.