I lost several hours and a lot of patience trying to get a Turkish e-Visa. The problem was that none of my email addresses could receive the confirmation email. Trip Advisor has many others with the same problem.
I solved this problem by using my work email. Other people have created a Gmail account for the purpose.
The headers in the email I received showed,
“Received-SPF: Fail (protection.outlook.com: domain of evisa.gov.tr does not
designate 188.8.131.52 as permitted sender)”
I suspect that many ISPs will block it from their network as spam. The email hosting provider could fix this by updating their DNS records as discussed here,
Alternatively they could change email provider to one like SendGrid or Amazon SES.