TheEdited after Ian Robertson Response.
The problem with the compiler is fixed in a newer version. You can try to reinstall the compiler first before you edit your csproj file.
Update-Package Microsoft.CodeDom.Providers.DotNetCompilerPlatform -r
Original:
The problem with the default VS2015 templates is that the compiler isn't actually copied to the tfr\bin\roslyn\ directory, but rather the {outdir}\roslyn\ directory
Add this code in your .csproj file:
<Target Name="CopyRoslynFiles" AfterTargets="AfterBuild" Condition="!$(Disable_CopyWebApplication) And '$(OutDir)' != '$(OutputPath)'">
<ItemGroup>
<RoslynFiles Include="$(CscToolPath)\*" />
</ItemGroup>
<MakeDir Directories="$(WebProjectOutputDir)\bin\roslyn" />
<Copy SourceFiles="@(RoslynFiles)" DestinationFolder="$(WebProjectOutputDir)\bin\roslyn" SkipUnchangedFiles="true" Retries="$(CopyRetryCount)" RetryDelayMilliseconds="$(CopyRetryDelayMilliseconds)" />
</Target>
