In November 2012 at a meeting at the A4A offices the FAA was asked:

Question:  Confirm that the flight time 1,000 hour in 365 consecutive calendar day cumulative limit begins on January 4, 2014, so that the initial 365 day period under part 117 will run from January 4, 2014 to January 4, 2015.  This is important because up until January 4, 2014, carriers will be complying with the current limits – 1,000 hours in a calendar year.  
 
FAA Answer: No, on January 4, 2014  the FAA will expect carriers to look back 365 days to January 4, 2013 for this cumulative limit.

Here is the extract from the 05-Mar-13 Letters of clarification.
If we look at the applicability section we find:

II.Discussion
A. Applicability
iii. Part 91 Flights

We note, however, that the cumulative limitations set out in 117.23 include “all flying by flightcrew members on behalf of any certificate or 91K Program Manages.”  Thus, even if a part 91 flight is not operated pursuant to part 117, that flight still counts for the purposes of the cumulative limitations of part 117 if it is flown on behalf of a certificate holder or 91K program Manager.

Since that time I have become aware that the FAA has been verbally advising air carriers the following:

On 4 January 2014 Part 117 limits begin. Part 117 is not retroactive. Therefore, we cannot hold you to any limit of part 117 prior to 4 January 2014. The look back begins on 4 January 2014 with a 10-hour rest look back. Now, this does not apply if you are doing early implementation. In this case your early implementation date would be your effective date; thus, the limitations begin on that date.

In essence, all flight operations that have been attributed to pre-part 117 operations will not count towards the cumulative limits under part 117. To put it another way the look back periods (168 hrs / 672 hrs and 365 calendar days ) for any of the cumulative limitations will not begin earlier than 00:00 04-Jan-2014.

The FAA through the Chief Counsels Office and Aviation Inspectors Office are working up a final explanation.