You are migrating a SharePoint Server 2010 My Site site collection to SharePoint Server 2013 by using the database attach method. You copy the content databases to the SharePoint 2013 farm. You need…

Site collection health checks run against an already-mounted and upgraded site collection in SharePoint 2013, not against a database that has not yet been attached or upgraded.

Test-SPContentDatabase analyzes a content database against the SharePoint 2013 farm without actually mounting or modifying it, reporting any missing features, site definitions, or assemblies that must be present before a successful upgrade can occur. Running it on the 2013 farm is correct because that is the target environment where the components must exist.

Running Test-SPContentDatabase on the SharePoint 2010 farm checks compatibility against the 2010 environment, not the 2013 target farm, so it cannot verify that 2013 has all required objects.

Health checks in the SharePoint 2010 site collection validate the source environment and do not verify readiness of the SharePoint 2013 destination farm.

Mount-SPContentDatabase on the SharePoint 2010 farm is not a valid step; mounting should only occur on the destination 2013 farm and only after verification with Test-SPContentDatabase.

Mount-SPContentDatabase on the SharePoint 2013 farm is the step that actually attaches and upgrades the database, which should only be done after Test-SPContentDatabase confirms all required objects are present.