I have settings configured in both Agent > Agents > Configure Agents > Agent Menu as well as Policy Management.
It seems that the settings are being applied via Agent > Agents > Configure Agents > Agent Menu only.
How can I make sure that Policy Management settings always override the local Agent module settings?
The way to make sure that Policy Management settings take effect is to stop defining settings locally. Local settings override policy, not the other way around.
Once you start using policies, EVERYTHING should be set with policies to prevent overrides and conflicts so that you know things are set as desired. Policies should always be "green" - if they're orange, somebody has manually created an override, and you have no way of knowing if the override is desired or not.
VSA Policies are like a polite 5 year old - they'll ask you to perform a task but go tattle if you don't. Contrast that to AD Group Policies, which are like the neighborhood bully. They'll demand that you do something and come back every 90 minutes to make sure you comply.