The Add Join tool does not correctly honor the definition query on the join table.

Workaround

Use the Make Query Table tool to create the filter or export the filtered table.

1. In ArcGIS Pro, search for and select the Make Query Table tool.
2. Select the table for Input Tables.
3. For Fields, select all fields from the data table.
4. For Expression, filter for the desired date. Click Run.
5. A 'QueryTable' table is added to your project.
6. Perform a join between the feature and the QueryTable table. Copy the contents of the field.

Steps to Reproduce