This is the key text from the MET2013 variable description:
Inexact Correspondence with Official Delineations
The protocol used by MET2013 is to identify the metro area in which the majority of each PUMA’s population resided. If MET2013 identifies a metro area for a given household, it indicates that, for the PUMA in which the household resided, a majority of the PUMA’s 2010 population resided in the identified metro area.
Match Errors and Code Suppression
MET2013’s code assignment protocol yields errors of omission (residents of a MSA who are not identified as residents) and errors of commission (non-residents who are identified as residents). PUMAs often nest well within metro area boundaries, resulting in small match errors, if any. For many metro areas, however, especially smaller metro areas, the intersecting PUMAs are a poor match.
As an index of mismatch, IPUMS uses the sum of percent omission error (the portion of an MSA’s population residing in excluded PUMAs) and percent commission error (the portion of the population in associated PUMAs that did not reside in the MSA).
For each reported MET2013 code, the MET2013ERR variable identifies the level of the sum of errors. Researchers may use MET2013ERR to impose a more restrictive error limit if desired.
Imagine a Venn diagram. The metro area population is in one circle. The population of PUMAs associated with the metro area are in another circle. Some population may be in the metro area but not in the associated PUMAs (omission error) and some may be in the PUMAs but not in the metro area (commission error). Does that help?
We use block populations in our computations only for the 2011 and earlier ACS samples, when we need to estimate the 2010 populations of intersections between 2000 PUMAs and 2013 metro areas.