There are unfortunately known issues in Visual Studio that don't have a workaround.
Checking the Refresh Table Data from the Advanced Options button of the TableAdapter Configuration Wizard looks like it works, but Visual Studio never passes those values to VistaDB. The dialog is hard coded to look only for Microsoft providers and send the value on to them, for all others the value is thrown away.
The only way to get a refresh on your data is to manually edit the SQL syntax and tell it to pull the data after an insert using a select statement.
Or you can add the select statement to the TableAdapter insert command at runtime in your application.
The SqlDataSource is designed for Sql Server. If your type does not match the exact namespace of the SqlClient several options don't work correctly.
DeriveParameters does not call the provider, it is hard coded only for Microsoft products. So all of the parameters in the Visual Studio Query Builder don't work correctly unless you implement a ? as the parameter type (even though ado.net allows the provider to specify this value, it is never used). ParameterPrefix is always an empty string for all providers except SqlClient.