Found on the Console > Settings > All Settings > Agents/Plug-ins > Software > Patch Management > Windows > Default Software Update Plug-in Policy (see the attached TECH127404.jpg for the full-size image):
 

Each of the circled Notification Types can have a custom text input, or use the default, and enable the check box for that type.
Then Set the interval in which each is desired to be repeated as applicable. Some items are a run once, so they have no interval settings.

Software Update Restart Notifications:

     Has 3 different settings. Ensure only one of these are used, for if multiple options are enabled, there will be conflicts on the client that may result in no popup displayed.

Show Reminder Messages setup:
          If set to run 'On Schedule'
               1. Ensure the 'Start / End' times are configured.
               2. Ensure the 'Duration' is configured.
               3. Ensure the 'During Window, check every:' setting is configured.
               4. Ensure the ''Repeat' setting is configured.
               5. If 'Advanced' settings are enabled:
                    Ensure the 'Start / End' dates are configured.
                    Note: This is for specific dates and will need to be verified for each scheduled update cycle.

Advisory: This setting will not produce a Reminder popup on the client to if the reboot schedule is set to run 'At the end of the Software Update cycle.'   

This is due to the client running the 'Schedule Reboot Reminder Scheduled Task' following the Software Update Cycle, but the Altiris Agent will change state of the client to reboot before the check commences. This is due to the Software Update Cycle ending and the reboot schedule is followed.
  This setting is mainly used in conjunction with the Reboot Schedule:'Never'
  This will give a reminder to the user that a reboot is needed.

Allow User to Defer: Will produce the Deferral popup on the client, for that allows the user to defer the reboot, even if the setting is 'At the end of the Software Update Cycle'

• This popup will allow for the smaller increments that lead to the larger maximum deferral period via the dropdown in the Notification Popup. This is to allow the end user the option of deferring for any period of time they choose until the maximum deferral time configured in this option is reached.
  • ​Note: This popup will display up to 4 days under the radial drop down 'Remind me later' and will allow for the full number of days/weeks as that time approaches, but reminds the user in those increments as it goes until the max increment is reached per the configuration on the policy.
  • Enhancement added for ITMS 8.0: Reboot Deferral popup is executed for max time, and in this version; the reboot reminder will popup again right before the reboot.

Enhancement Request & Usability Review: Submitted for review by Symantec Inc. to have the Deferral popup allow for later reboot and allow for the Reminder popup to run as scheduled in the meantime to ensure the end user is constantly updated that the reboot is pending.

Note: Notification popups will last on the client for 5 minutes as this is controlled by the Altiris Agent design and is held in the client's registry: HKLM > Software > Altiris > Altiris Agent key; and the value is set to 5 (mins) on the 'Notification Countdown Period' and at this time the setting is not editable. Additionally, another configuration for Client Settings regarding notifications can clash with this configuration as detailed on KM: TECH179974.

Confirmed: Patch Management notification popups still occur if the Client's Altiris Agent icon is hidden from the systray.

Caution: Having the configuration enabled for 'Allow immediate restart if required' enabled on any Software Update Policy will cause each bundled update to throw a reboot notification multiple times (one for each install from that policy) on the targeted client.