After much digging around I found errors in a few of the *.bat (nokogiri, scss,...) files located in C:\path\to\RailsInstaller\Ruby2.2.0\bin.
This was the content of rails.bat:
@ECHO OFF
IF NOT "%~f0" == "~f0" GOTO :WinNT
@"C:\Users\emachnic\GitRepos\railsinstaller-windows\stage\Ruby2.2.0\bin\ruby.exe" "C:/Users/emachnic/GitRepos/railsinstaller-windows/stage/Ruby2.2.0/bin/rails" %1 %2 %3 %4 %5 %6 %7 %8 %9
GOTO :EOF
:WinNT
@"C:\Users\emachnic\GitRepos\railsinstaller-windows\stage\Ruby2.2.0\bin\ruby.exe" "%~dpn0" %*`
After removing the hardcoded paths C:\Users\emachnic\GitRepos\railsinstaller-windows\stage\Ruby2.2.0\bin\, the rails command reports the correct version:
C:\path\to\RailsInstaller3.2\Ruby2.2.0\bin>rails -v
Rails 4.2.5.1