Hi-- I asked Nate Mantua (now with NOAA) about this index and he confirmed to me that global warming signal is likely impacting this version of the PDO index. The influence is not large, but it is probably enough to transform some of those small, positive PDO values in recent years into negative PDO values.  

"Neutral" is a designation of "near average."  For ENSO, we designate -0.5 to +0.5 (Nino-3.4 index) as Neutral, but these thresholds are somewhat arbitrary.  The same can be done for the PDO index, but I'm not aware of any effort to define thresholds for this index.