I don't use Cygwin, but I guess that all Cygwin programs run their output through an ANSI escape interpreter, while the Win32 Perl does not.
This would explain why you see the ANSI escapes interpreted with Cygwin Perl but raw with the Win32 Perl.
You can "fix" this by loading the module Win32::Console::ANSI in your program, which interprets the output as ANSI and instructs the Windows console to render it properly. Of course that means you should only load that module on "real" Win32 Perl, not Cygwin Perl.
use if $^O eq 'MSWin32', 'Win32::Console::ANSI';