Expected behavior when Clear-Site-Data header is set?

Is this suppose to happen instantly or after some time, or I am just missing some else?

It is supposed to happen instantly. The (draft) spec states:

If the Clear-Site-Data header is present in an HTTP response received from the network, then data MUST be cleared before rendering the response to the user.

Additionally, as you mention in this comment it is only supported when a request is secure (either https or localhost).

I prepared a simple test, with two resources:

• index.html -- a page that links to a CSS file, and also accepts a ?clear query parameter to include a CSD header in the response
• style.css -- a CSS page with random colours, to make clear when it has been regenerated, that declares itself as cacheable

This behaved as specified with Firefox 76.0.1; on receiving a resource with Clear-Site-Data: "cache", the cache is cleared before fetching its subresources.

Without Clear-Site-Data:

• Fetch index.html by entering the URL and hitting Enter
• Repeat this. Note that the referenced style.css is served from the cache, and the page colour doesn't change

With Clear-Site-Data:

• Fetch index.html?clear by entering the URL and hitting Enter
• Repeat this. Note that the referenced style.css is not served from the cache, and the page colour changes

Code:

#!/usr/bin/python3

import http.server
import socketserver

import random

PORT = 8000

class SampleDataHandler(http.server.SimpleHTTPRequestHandler):

    def do_GET(self):
        if ".css" in self.path:
            self.send_response(200)
            self.send_header('Content-Type', 'text/css')
            self.send_header('Cache-Control', 'max-age=3600')
            self.end_headers()
            color = b"%06x" % random.randint(0, 0xFFFFFF)
            self.wfile.write(b"html{background-color: " + color + b";}\n")
        else:
            self.send_response(200)
            if '?clear' in self.path:
                self.send_header('Clear-Site-Data', '"cache"')
            self.end_headers()
            self.wfile.write(b"<link rel=stylesheet href=style.css>This is the content.\n")


httpd = socketserver.TCPServer(("", PORT), SampleDataHandler)

httpd.serve_forever()