When a user replies to an email the Updated(sys_updated_on) field on the target record is not updated, though the record activity log shows the email associated with the record.
An Inbound email to ServiceNow by default does not update any fields until you create an Inbound Email action to handle the incoming email and update any field on the target record.
Activity logs on the record will display the email as the email is only associated to the record (based on the reply message). Even if there is no inbound email action process the email will show up in the activity logs but this is not considered as an actual update as there is no update on the target record fields.
To update the "Updated" field on a record, create an "Inbound Email Action" on the related table and update any of the field in the Inbound Email Action/script
current.comments = "reply from: " + email.origemail + "\n\n" + email.body_text;
Activities on a record is customizable and you can turn it 'off' and 'on' (Click on the "Filter Activities" Funnel icon next to actives on the incident record and uncheck "Sent/Received Emails").