This behaviour is by design. When you use RgPublish to publish a .csproj, it uses MSBuild to build the project, and therefore gives you exactly the same output that building in Visual Studio would give you.
If you want referenced assemblies to be deployed to the target location, you need to set CopyLocal on those assemblies to true, otherwise the assumption is that they are installed in the GAC. Is there are reason you need some assemblies not to be copied to the output directory for local builds, but do want them deployed to the target directory on deployment?
There is no harm in deploying .pdbs - in fact, it helps with debugging exceptions on live systems - but if you want to remove them, you can turn off pdb generation by right-clicking on the project in Visual Studio, going to Properties...->Build->Advanced... and setting the 'Debug Info' dropdown to 'none' for the Release configuration.
If you want to do more specific filtering of the output so that the deployed files are not the same as the build output, you'll need to switch to using RgPublish with a .nuspec file after building the project