The NOTIFY= <logonid> in the JCL JOB statement will not work if the ACF2 logonid record for the user has NOINTERCOM specified.
The NOTIFY= <logonid> parameter on the JCL JOB statement, or the JECL /*NOTIFY statement will cause the $HASP165 message to be displayed, via the SEND command, to an interactive user when the job ends.
The ACF2 TSO INTERCOM|NOINTERCOM logonid field controls whether a TSO user is willing to receive messages sent via the TSO SEND command. If NOINTERCOM is specified in the ACF2 logonid record for the TSO user, the $HASP165 NOTIFY message will not be received.
Details on the ACF2 TSO INTERCOM|NOINTERCOM logonid field can be found in the ACF2 for z/OS Administrator Guide, in Chapter 3: Maintaining Logonid Records, section "Logonid Record Fields".
Details on the JES2 $HASP165 message can be found in the IBM Z/OS JES2 MESSAGES Guide.