Can I update/requery a custom field that got changed via another field on the same page?
The contact summary screen is divided into different panes, and they are each refreshed separately. If a popup form needs to refresh one or more panes, it can specify them by jQuery selector. For example, the relationship form has this in its post-process function:

$this-&gt;ajaxResponse['reloadBlocks'] = array('#crm-contactinfo-content');


Which has the effect of refreshing the pane that contains, among other things, the current employer (which the relationship form may affect).

When you implement this in your form hook it will look like:

function ccas_hooks_civicrm_postProcess($formName, &amp;$form){
  if ($formName == 'CRM_Contact_Form_Inline_CustomData') {
    $form-&gt;ajaxResponse['reloadBlocks'][] = '#crm-contactinfo-content';
  }
}


Or substitute/add the jQuery selectors of whichever other blocks you'd like to see refreshed. Note that this code uses the array append syntax rather than overwriting the entire array.