Indeed, Michael.

Here is a proposal for a solution:

<result>{
  for sliding window $w in $seq/stream/event 
    start $s when $s/person = "Anton" and $s/direction = "in"
    only end $e when $e/person = "Barbara" and $e/direction = "in"
  where xs:dateTime($e/@time) - xs:dateTime($s/@time) < xs:dayTimeDuration("PT1H")
  return 
    <warning time="{ $e/@time }">Barbara: Anton arrived 1h ago</warning>
}</result>

Notice the "sliding" instead of tumbling.
Probably the "where" could also be replaced by a "and" with the "only end" condition.

The solution from Franc might cause several notifications. I would propose: 

declare variable $seq := fn:doc("person_events.xml");

<result>{
  for tumbling window $w in $seq/stream/event 
    start  $s when $s/person eq "Anton" and $s/direction eq "in"
    only end $e next $n when  xs:dateTime($n/@time) - xs:dateTime($s/@time) gt 
      xs:dayTimeDuration("PT1H") 
      or  ($e/person eq "Barbara" and $e/direction eq "in") 
      or ($e/person eq "Anton" and $e/direction eq "out")
  where $e/person eq "Barbara" and $e/direction eq "in"
  return 
    <warning time="{ $e/@time }">Barbara: Anton arrived 1h ago</warning>
}</result>

For the current working draft I used my solution and I mark this bug FIXED.  Mike, if you agree with my solution, please mark it CLOSED.