How to change a value of a custom object based on a parent standard object value

Summary:

We have the serious need to update a custom object that is related to a parent standard object. In this case it is specifically

Content (required):

Mobile assessments are updated for status when the mobile app downloads or uploads an assessment. However, our users also use the OSvC/OIA container to run the OIA models in RightNow and BUI. When they do this, the mobile assessment status is not updated when the assessment is submitted through RightNow/BUI. This means that it will then get synced down to an agent's mobile device the next time he/she syncs their device even though the assessment is complete. We need to be able to have the mobile assessment status updated when the status on the assessment changes, but I