Yes, FHFA uses the revised Metropolitan Statistical Areas (MSAs) and Divisions as defined by the Office of Management and Budget (OMB) in February 2013 (and revised in July 2015, August 2017, and April 2018). These MSAs and Divisions are based on Census data. According to OMB, an MSA comprises the central county or counties containing the core, plus adjacent outlying counties having a high degree of social and economic integration with the central county as measured through commuting. For information about the current MSAs, please visit:
Prior to the second quarterly release in 2013, FHFA produced metropolitan area indexes based on the December 2009 delineations provided by the OMB at https://www.whitehouse.gov/sites/whitehouse.gov/files/omb/bulletins/2010/b10-02.pdf
That quarter's Highlights piece explains the transition from the December 2009 to the February 2013 definitions. HPIs constructed from both the 2009 and 2013 delineations are available on the Downloadable Data page under the "Additional Data" section then the "Utility Files and Background Information for Index Construction" subsection.