You can send mail by php function or SMTP ,if you select PHP as method for sending emails ofcourse it doesn't use zoho mail server..infact it doesn't use any mail server...it is sent using php mail function.If you want to send emails with mail server you have to select SMTP and configure mail parameters properly ....username,password,hostname and port.I'm using office365 and didn't use zoho for quite long but as I remember you have to whitelist IP address in zoho control panel.
mail class is in blesta/components/email/email.php but you can't just set dkim signature and expect just to work...you have to add key to your MTA ..it is easier for you to set SMTP ....and may I ask why you can't send emails from your hosting account in first place...
Here is instructions from their site...as you see sending mail must match authentication email,so if you want to send emails from noreply@yourdomain.com and you are authenticate with admin@yourdomain.com or any similar usecase than you have to add sending mail as alias..also make sure to whitelist main server IP and hosting account IP (if are not same)
SMTP Configuration settings for Zoho Mail - SSL
Outgoing Server Name: smtp.zoho.eu
Port: 465
Security Type: SSL
Require Authentication: Yes.
The email address should match the email address/ aliases of the account, for which the authentication details are provided.
SMTP Configuration settings for Zoho Mail - TLS
Outgoing Server Name: smtp.zoho.eu
Port: 587
Security Type: TLS
Require Authentication: Yes. The email address should match the email address/ aliases of the account, for which the authentication details are provided