DONOTCACHEPAGE isn’t working

I’m trying to set up a custom field (via ACF) to allow my users to enter a URL to redirect to. This is working fine on the first load, but WP Super Cache is then generating the cached page, even though I have define("DONOTCACHEPAGE", true) set. Here’s the full redirect code:

<?php
$redirect = get_field("redirect");
if ($redirect) {
    define("DONOTCACHEPAGE", true);
    wp_redirect($redirect, 301);
    exit;
}
?>

This is at the top of my header.php, but I’ve also tried moving it to the top of my page.php, with no luck. I don’t see why this wouldn’t work, any help would be greatly appreciated.