The complicated thing is we have integrated mandrill to send out the emails, so while sending we do not use zoho servers instead mandrill send the emails for us. 

However, we do access received emails from zoho panel. Since the email address is hosted by zoho.

This is just to clarify, will zoho email sending limits apply in this case too? (like no of emails / day)

Does each time any external service sends out an email on our behalf , is count to be sent by zoho? 

We have created seprate DKIM record and added spf record as follows 

" v=spf1 mx include:zoho.com include:spf.mandrillapp.com ~all"

Regards