I can't emphasize how important it is that documents considered invalid or documents considered "obsolete" (not yet expired, but obsolete in purpose) are removed when you have changes under NEXUS. The TTP site reflects the updates, at least from the US side, but not necessarily the Canadian side.
My experience: I was born in the US, one parent was a US citizen, other was US LPR born in Canada (Canadian citizen). Up until 2017 I didn't apply for any proof of citizenship. I went for GE in 2013 and NEXUS in 2016 on the basis of travel between US/CAN for work. When I applied for both GE & NEXUS, I had no Canadian citizenship certificate or Canadian passport, thus I wasn't considered Canadian.
When I got NEXUS in 2016, I had US Passport + a Canadian work permit obtained at the Canadian border (point of entry). They punched it in the system, and then I was good using the NEXUS kiosk.
Fast forward to 10 days before my work permit expires. NEXUS Receipt is IMM 1-1 (proceed directly to secondary customs). Wait 30 minutes. Officer says everything looks peachy. Go to fly home 6 days before end of work permit. Flight gets cancelled, next flight is tomorrow, have to re-enter Canada to get a hotel overnight. NEXUS kiosk says IMM 1-1. Secondary officer says everything looks fine. Fly up to Canada after my work permit has actually expired for a business meeting (meetings without productive work being done are exempt under NAFTA from needing a work permit). IMM 1-1 again. Wait an hour to see an officer who again tells me everything looks peachy, nothing wrong.
Finally get a new work permit (immigration firm took their time on the application package). Visit the NEXUS office to add the new work permit. Get told the NEXUS kiosks automatically secondary anyone who has a work permit that is about to expire or has expire, and the only people who can see that this is the reason for it OR clear the block is the NEXUS office. Also, the addition of adding a new work permit doesn't automatically remove the block from an old work permit (they're supposed to do it at the NEXUS office, so I'm told). This only affected the NEXUS CBSA computers since the work permit had to do with my purpose of entry to Canada (as a US citizen I could enter the US for any purpose).
Get my Canadian Citizenship certificate in September 2017, add it at the NEXUS office at YYZ next time I fly in. They mention to me that I'll need to make a second trip when I get my passport, and they'll leave the work permit on there in the interim so my next entry to Canada via NEXUS will work. Get my passport in the mail at the end of September, when I next visit YYZ in October I add the Canadian passport. I mention asking if I need the work permit on my profile anymore and all the hassles I had when my last one expired, CBP & CBSA officers remarked that "oh yeah, it should be removed". They removed it.
If you have US citizenship and add Canadian nothing changes in terms of the card. If you had US LPR/Canadian PR status and then got Canadian citizenship, I imagine they'll probably issue a new card.
Good luck and let us know how things go.