Are you saying if you run that second search in a different app context, the behaviour is different. Note that your SPL logic to do stats earliest(_time) as min_time will not tell you the actual search range, just the time of the earliest event it found. Try the SPL ...
| stats min(_time) as min_time max(_time) as max_time by index
| convert ctime(min_time) ctime(max_time)
| addinfo The addinfo command will show you the actual search range used by the search irrespective of any events found.
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