To have your email account working with Hostinger you only need to do a few easy steps:
Point your domain to Hostinger (with either NS or A record)
What to do if your domain is using external nameservers?
If your domain is pointing elsewhere by NS records, your DNS Zone management is moved to the provider you pointed the domain to and should be managed from there.
As long as your domain is pointing to Hostinger by A record, the changes you should do to your active DNS zone can be found in the Email Deliverability section:
After records are set, it may take up to 24 hours for them to propagate
What to do if my cPanel domain is pointing elsewhere via A record?
Add cPanel MX records: since MX records of cPanel point back to your server IP, to use email services with us follow this procedure:
Create a subdomain (for example, mails)
Point the subdomain to your cPanel’s hosting IP address here at Hostinger via A record
Point your domain’s MX record to the newly created subdomain
Once this is done your MX records will be pointing to our server 👍
cPanel TXT (SPF) record: the required TXT (SPF) record for cPanel can be found inside your DNS Zone Editor, just copy the record and add it to your active DNS Zone.