TWebFilePicker upload from https?

I'm playing around with the TMS WEB Core Demos\Basics\Upload demo.
Works great on http websites but on https websites I get an error:
Make sure the uplaod server is running

Are there any know issues with uploading from https sites?
Or am I missing any configuration in UpdateHandler or the web part?

No known issues. The upload server needs to be bound to HTTPS and the proper URL needs to be used.

I can't get it to work.
Port is bound, I receive a request (Tested in IdHTTPServer1QuerySSLPort, but after that - nothing).
Maybe it's Indy, maybe not.
I'll try with ICS components.