The CALDBVER keyword isn't set by the CIAO tools, it is set in the pipeline. It is not, therefore, automatically updated by acis_process_events.

If you would like to manually change the value, e.g. to recall later what version was used in reprocessing the data, use dmhedit:

unix% dmhedit infile="acis_new_evt2.fits" filelist="" operation="add" \
      key="CALDBVER" value="2.23" datatype="indef" unit="" comment="CALDB version"

The Note on Processing Versions shows how to determine what version of the CALDB is installed on your system.