FULL PRODUCT VERSION :
java version "1.8.0_102"
Java(TM) SE Runtime Environment (build 1.8.0_102-b14)
Java HotSpot(TM) 64-Bit Server VM (build 25.102-b14, mixed mode)

ADDITIONAL OS VERSION INFORMATION :
Window 7/64-bit

A DESCRIPTION OF THE PROBLEM :
The java.time.zone.ZoneRules have inconsistent previous / next transition handling at a transition instant time. Even the transition instant time correcly represents the new transition offset the previous transition has not been changed.

This breaks following invariants
previousTransition.OffsetAfter == nextTransition.OffsetBefore
previousTransition.OffsetAfter == Offset

The previousTransition method should be rather specified as
"Gets the previous transition before or at the specified instant"

STEPS TO FOLLOW TO REPRODUCE THE PROBLEM :
import java.time.Instant;
import java.time.ZoneId;
import java.time.ZoneOffset;
import java.time.zone.ZoneOffsetTransition;
import java.time.zone.ZoneRules;

import org.junit.Assert;
import org.junit.Test;

public final class ZoneRulesPreviousTest {
  @Test
  public void testPreviousEuropeBerlinZone() {
    final Instant now = Instant.now();
    final ZoneRules zoneRules = ZoneId.of("Europe/Berlin").getRules();
    final Instant transitionInstant = zoneRules.nextTransition(now).getInstant();
  
    // BEFORE TRANSITION
    {
      final Instant beforeTransitionInstant = transitionInstant.minusMillis(1);
      final ZoneOffset offset = zoneRules.getOffset(beforeTransitionInstant);
      final ZoneOffsetTransition prevTransition = zoneRules.previousTransition(beforeTransitionInstant);
      final ZoneOffsetTransition nextTransition = zoneRules.nextTransition(beforeTransitionInstant);
      Assert.assertEquals(prevTransition.getOffsetAfter(), nextTransition.getOffsetBefore());
      Assert.assertEquals(prevTransition.getOffsetAfter(), offset);
      Assert.assertEquals(nextTransition.getOffsetBefore(), offset);
    }
  
    // AFTER TRANSITION
    {
      final Instant afterTransitionInstant = transitionInstant.plusMillis(1);
      final ZoneOffset offset = zoneRules.getOffset(afterTransitionInstant);
      final ZoneOffsetTransition prevTransition = zoneRules.previousTransition(afterTransitionInstant);
      final ZoneOffsetTransition nextTransition = zoneRules.nextTransition(afterTransitionInstant);
      Assert.assertEquals(prevTransition.getOffsetAfter(), nextTransition.getOffsetBefore());
      Assert.assertEquals(prevTransition.getOffsetAfter(), offset);
      Assert.assertEquals(nextTransition.getOffsetBefore(), offset);
    }
    
    // AT TRANSITION
    {
      final Instant atTransitionInstant = transitionInstant;
      final ZoneOffset offset = zoneRules.getOffset(atTransitionInstant);
      final ZoneOffsetTransition prevTransition = zoneRules.previousTransition(atTransitionInstant);
      final ZoneOffsetTransition nextTransition = zoneRules.nextTransition(atTransitionInstant);
      Assert.assertEquals(prevTransition.getOffsetAfter(), nextTransition.getOffsetBefore());
      Assert.assertEquals(prevTransition.getOffsetAfter(), offset);
      Assert.assertEquals(nextTransition.getOffsetBefore(), offset);
    }
  }
}


REPRODUCIBILITY :
This bug can be reproduced always.