The failing test cases:

src/test/java/org/joda/time/TestDateTimeZoneCutover.java:1249-1263
public void testBug3476684_adjustOffset() {
    final DateTimeZone zone = DateTimeZone.forID("America/Sao_Paulo");
    DateTime base = new DateTime(2012, 2, 25, 22, 15, zone);
    DateTime baseBefore = base.plusHours(1);  // 23:15 (first)
    DateTime baseAfter = base.plusHours(2);  // 23:15 (second)
    
    assertSame(base, base.withEarlierOffsetAtOverlap());
    assertSame(base, base.withLaterOffsetAtOverlap());
    
    assertSame(baseBefore, baseBefore.withEarlierOffsetAtOverlap());
    assertEquals(baseAfter, baseBefore.withLaterOffsetAtOverlap()); // <-- TC fails here
    
    assertSame(baseAfter, baseAfter.withLaterOffsetAtOverlap());
    assertEquals(baseBefore, baseAfter.withEarlierOffsetAtOverlap());
}

The faulty code:

Line is covered but NOT in slice
Line is covered and in slice
Line is in slice but NOT covered
src/main/java/org/joda/time/DateTimeZone.java:1163-1180
public long adjustOffset(long instant, boolean earlierOrLater) {
    // a bit messy, but will work in all non-pathological cases
    
    // evaluate 3 hours before and after to work out if anything is happening
    long instantBefore = convertUTCToLocal(instant - 3 * DateTimeConstants.MILLIS_PER_HOUR);         //<-- BUG!! 
    long instantAfter = convertUTCToLocal(instant + 3 * DateTimeConstants.MILLIS_PER_HOUR);          //<-- BUG!! 
    if (instantBefore == instantAfter) {                                                             //<-- BUG!! 
        return instant;  // not an overlap (less than is a gap, equal is normal case)
    }
    
    // work out range of instants that have duplicate local times
    long local = convertUTCToLocal(instant);                                                         //<-- BUG!! 
    return convertLocalToUTC(local, false, earlierOrLater ? instantAfter : instantBefore);           //<-- BUG!! 
    
    // calculate result
      // currently in later offset
      // currently in earlier offset
}

Other code:

src/main/java/org/joda/time/DateTime.java:664-667
public DateTime withEarlierOffsetAtOverlap() {
    long newMillis = getZone().adjustOffset(getMillis(), false);
    return withMillis(newMillis);
}
src/main/java/org/joda/time/DateTime.java:684-687
public DateTime withLaterOffsetAtOverlap() {
    long newMillis = getZone().adjustOffset(getMillis(), true);
    return withMillis(newMillis);
}