The requester notifications are sent for two status: 'Resolved' and 'Closed'
Both 'Resolved' and 'Closed' are default completed statuses. When a technician provides a solution that he thinks will solve the issue, he/she can set the request to the 'Resolved' status (Here, the technician uses this when no confirmation is received from the requester).
The requester can try out the solution and close the ticket or ignore it and resolved requests can be closed after a period of time if there is no response from the requester. This can be configured in Request Closure Rules.
'Closed' status can be used by a technician when he's provided a solution and has got the confirmation from the requester that the issue has been solved (maybe on a phone call or chat).
If you do not want closed requests to be reopened by requester's responses, please visit Admin > General Settings > Self-Service Portal Settings and modify settings such as "When the requester replies through E-mail / Portal to the closed requests. Perform the following:".