The differences between the web services console and Luminate Online are due to time zone differences.

Luminate Online is in CST by default, but you can confirm what time zone your instance is using through these steps:
  1. Edit a constituents profile  
  2. Click Save to save the changes.
  3. View the modification time on the constituents profile to determine which time zone the site is set to

The web services console will output date and time information that looks similar to this: 


The Z at the end of the time indicates the offset - "Z" as the offset means zero hour offset/Zulu time/UTC. 

The two times will need to be adjusted accordingly until they are in the same time zone. Please note that Daylight Savings Time may be affecting your Luminate Online times as well.