customizer dynamic stylesheet not showing live edits

Hi I am using this code but even with jquery it won’t live update the css, even on publish. I am using a dynamic css stylesheet rather than another bloat of css inline as WordPress adds its own as well does any plugin and theme.

add_action('parse_request', 'parse_dynamic_css_request');
function parse_dynamic_css_request($wp) {
$ss_dir = get_stylesheet_directory(); // Shorten code, save 1 call
ob_start(); // Capture all output (output buffering)
require($ss_dir . '/designer.css.php'); // Generate CSS
$css = ob_get_clean(); // Get generated CSS (output buffering)
file_put_contents($ss_dir . '/designer.css', $css, LOCK_EX); // Save it
}

function designer_customize_register( $wp_customize ) {

I am using customizer functions to create e.g. colors and it all works well and updates the designer.css stylesheet that I have enqueued.
Is it possible to see live changes? It shows up if I update and clear the browser cache but that is not the aim I want it to be dynamic or is this only going to work using inline css?
Thanks