The error message indicates that you are mixing static libraries built with one version of Visual C++ (VS 2013) with code built with a different version (VS 2015). This is because the Standard C++ Library cannot be 'mixed' in the same application.
If you are using VS 2015, then you should pick the appropriate vcxproj for your platform and toolset using project-to-project references:
DirectXTK_Windows10is for Windows 10 UWP built with VS 2015DirectXTK_Desktop_2015is for Windows desktop apps built with VS 2015 with 'down-level' compatibility for Windows 7DirectXTK_Desktop_2015_Win10is for Windows desktop apps built with VS 2015 that requires Windows 10 or later--this config mostly exists for test purposes.
See the DirectX Tool Kit wiki for details.
Note: I will be publishing NuGet packages for UWP and VS 2015 Windows desktopare now published for the next release of DirectX Tool KitUWP and Windows desktop.