Can you control who sees what data when using Power BI for analytics and dashborads?

Yes – the easiest way is to use a data source with Role Level Security (RLS), such as Analysis Services.  With RLS, the Power BI service will apply that role level security, and users who do not have sufficient credentials to access the underlying data (which could be a query used in a dashboard or report) will not see that data.

If a user’s access to the underlying data is different from the user who created the dashboard or report, the visualizations and other artefacts will only show data based on the level of access that user has to the data.  If you do not have a RLS data source, when data is shared with other users (such as through a dashboard or report), the original credentials are used to access or display the data.