I only had issues with mail from mailgun being flagged as spam if it was a new domain, once I had moved it from the spam folder to the inbox on gmail.com and outlook.com, it was never flagged as spam again.
confirmation mails can be tricky, often it is the content of the mail, rather than the mail setup that gets them flagged. adding some text, proper styling, and make a proper a href link text, will be better than just posting a raw link.
this service https://spamcheck.postmarkapp.com/ can help you check the content. and also check if your domain (or subdomain) has been blacklisted Email Blacklist Check - IP Blacklist Check - See if your server is blacklisted
the idea that subdomains has an increased chance of being flagged as spam makes no sense if the configuration is correct.