Hokuriku Shinkansen gates at Tokyo Station

Everything I’ve read so far about boarding the Shinkansen using tickets linked to Suica cards seems to suggest that when you tap in at the Shinkansen gate, a seat reservation ticket will print out of the gate, which one needs to take to avoid having to pay again on the train.

We just passed through the Hokuriku Shinkansen gate at Tokyo Station, and no such ticket appeared. What did happen though is I immediately received an email titled:
[You have passed the Shinkansen automatic ticket gate machine] Shinkansen seat number for 07/11 (JR tickets)

Right now we’re trying to relax in our swanky GranClass seats, but stressing out every time the conductor walks by.

Is the gate printout seat ticket only a thing when you use QR code tickets, scanned at some other Shinkansen stations???