In order to provide processing of your mail at the domain by a third party service (e.g. Yandex.Mail), you need to change MX record at the domain.
Find more about it in the instructions to these mail services. It is very simple.
1. Go in CPANEL.
2. Then, enter MX Records (this section is in the same place with e-mail accounts).
3. Choose a desired domain. After that, a list of MX records opens.
4. DELETE CURRENT RECORD.
5. Add a new one provided by mail service. For Yandex – mx.yandex.ru. Priority 10. Value: mx.yandex.ru
6. Save. Everything starts working. In some cases, in E-mail Routing it is necessary to specify – Remote Mail Exchanger. But usually everything works without it.