If this is the same issue as I encountered a few months ago (I really should have kept notes), then it's because the Files app ignores singleTask for launchMode and attempts to start a new activity, and Delphi does not support starting a completely new activity in the same app. This is an SO discussion about it being a problem also using Java.
I seem to recall that I was going to try and work around it by constructing an Activity in Java, and have it forward the intent to the Delphi app, not trying to start it again if it was already running, of course. I am yet to do anything like that as it's not a priority for me.