Propogation is done when you change nameservers so that your domain can map to your dns server. Subdomains are setup on the server itself, so as long as your domain is pointing to your nameserver, you do not have to wait for propogation. On the other hand you may need to clear your nameserver or wait for about an hour for the server to refresh and add the new records.
When you add a subdomain, you changes the DNS records on your DNS server. This change has to be propagated to rest of the global DNS servers for your subdomain to be accessible worldwide. So yes, you have to wait for a while.
Oceanworld is agreeing. The problem arises when you create the subdomain as each domain registrar has different TTL set for dns record expiration and same is the case with your webhost, if you are using webhost nameservers.
Usually the update takes about 15seconds to notice but it can be as long as a few hrs but not close to days.
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