Strange, your question does not have any relations to perl.

When I tried your situation on my computer, I got predicted behaviour, namely date commands with any redirections worked good.
I think our difference may be influented by cygwin versions, and remember there is a DOS-builtin date command which asks for a date to change, so you probably somehow got out of your cygwin environment and got into bultin (win?)DOS commands.

Best wishes,
I.R.Baboon.