Siri requires your permission before it will allow Next3Trains to return your trains this way. This should happen the first time you try and use Siri to have Next3Trains return anything. Once this is done, you can ask Siri for your next trains even if the app is not running (ie ask via voice when you’re in the car, pulling into the railway station parking).
If you’ve dismissed that prompt, or you later change your mind, you can always ask Siri while the app is open in the foregound - ask Siri to “Check my trains in Next3Trains”. This should also pop up the system prompt for permissions. If that doesn’t work, you can enable this via the Shortcuts app: from the Library view, scroll down to Next3Trains in the list of apps and click on it, press the (i) button, and ensure the Siri permission is enabled.