I have a Tiki 20.x clean installation on LAMP and I installed Composer via Tiki's web interface.
Going via the "Packages" feature in Control Panel, under the Diagnose tab there is an "install Composer" button.
Installing it through this route and then installing packages works for me, I see those packages installed when I run tiki-check.php.
Not sure whether Windows Server/IIS environment should make a difference.
What Tiki version are you running?