Hope you are doing well. Per the description, I understand you want to close a file with a time limit.
Since this is design behavior, you may need to remove the application from the app switcher to close the document. The same behavior is followed on the desktop version of the application.
Please fill out the feedback form if you think this is something to be added to the application for a better experience. Filling out this form ensures that your feedback reaches our product team for them to look into and try to implement it in the upcoming updates: https://acrobat.uservoice.com/.