To ensure that only employees can access their own records on the customer object and not their managers at Universal Containers, given that the Organization-Wide Defaults (OWD) are set to private, the most effective and direct approach is:

**A. Uncheck Grant Access using Hierarchies in Sharing Settings.**

Here’s why this option is suitable:

- **Grant Access Using Hierarchies**: Salesforce includes a default setting where managers in the role hierarchy can access records owned by their subordinates. This setting is typically enabled by default for standard and custom objects. If the goal is to ensure that managers do not have access to their employees' records, the administrator should uncheck this option for the custom object in question. This will override the default behavior and ensure that managers cannot access records owned by their direct reports unless explicitly granted by another sharing mechanism.

The other options are less relevant for the specific need to restrict manager access:

- **B. Verify that Allow Search is unchecked on the custom object.**
- While unchecking "Allow Search" would prevent the records from appearing in search results, it does not inherently restrict access to the records if someone navigates to them directly or if they have a direct link. This option doesn’t provide the necessary access control on its own.

- **C. Uncheck Allow Users to Access Privacy Data on each profile.**
- This option is not standard in Salesforce and does not directly correspond to controlling access to specific records based on hierarchy. It seems to be a misunderstanding of Salesforce features or possibly a custom implementation.

- **D. Enable Hide Personal Information in User Management Settings.**
- This option relates to hiding personal information across the user interface but does not impact access control to specific records or override hierarchical access settings.

Therefore, the correct and effective action to take is **A. Uncheck ...