Question:

Where is the symbology controlled for the active horizontal alignment?

Answer:

The points styles for Active Geometry are controlled by the styles that are defined on the Styles tab of the View Horizontal Annotation command.  If these styles do not exist, the point symbology will be determined by the Default style.  Assuming these styles DO exist, you can change the symbology in Tools>Style Manager.  Select the style, click "edit". On the Edit Style>General leaf, make sure "Geometry Point Feature" is toggled on.  On the Edit Style>Geometry Feature>Points>Symbology leaf, select the desired named symbology.  You can also edit the symbology from here if you would like.