Not exactly - from the original Nagios definition comes this
first_notification_delay: This directive is used to define the number of "time units" to wait before sending out the first problem notification when this service enters a non-OK state. Unless you've changed the interval_length directive from the default value of 60, this number will mean minutes. If you set this value to 0, Nagios will start sending out notifications immediately.
Here i would say it is more time since last time ok state. That would be valid in all your logs. Every log shows 30 minutes since last ok.