This thread was very helpful as we waited for our applications to be processed so I thought I would share our experience.

Initial online application: May 4, 2018 (2 adults and 2 children)
Conditional Approval: My wife received hers June 20, 2 kids on June 21 and me on June 22. (this was also the order which we applied) Approximately 32 to 34 business days.
Interview: July 17 for all 4 of us (YEG). This process took approximately 20 minutes for all 4 of us plus about 15 minutes waiting time.
Approved for Nexus: July 17 (received email upon leaving interview as other members have experienced)
Cards Received: July 31, 2018

Overall the process was very smooth and just under 3 months from application to cards in hand.