I heard LSV saying there is a distinct difference with day/night mechanic vs werewolf mechanic. From what I’m seeing they pretty much seem the same. No spells causes the werewolves to flip (become night) and two spells flips them back to the front side (back to day).
The big difference is when it’s night things come etb as the backside.
The day-and-night mechanic is separate from the abilities—
"At the beginning of each upkeep, if no spells were cast last turn, transform [this permanent]", and
"At the beginning of each upkeep, if a player cast two or more spells last turn, transform [this permanent]".
The mechanics article, though, didn't state whether transforming double-faced cards with either ability will replace that ability with daybound or nightbound, respectively. Thus, it can be presumed that those cards won't change in this respect with the upcoming set.
Daybound and Nightbound changes the state of the game to Day or Night respectively. This is a quality of the game itself and the change happens in the untap step, not upkeep. And as soon as the game changes, the werewolves transform immediately. There is no trigger and nothing to respond to: they just happen.
Also, the original werewolf mechanic cares about all players: the human-werewolf side transforms if no player at all cast any spell during a turn, and the just-werewolf side transforms if any player casts two or more spells in any turn.
The new mechanic cares only about how many spells the active player casts. Spells cast by other players during your turn don't count either way.
And, as already said, being night or day is a "trait" of the game itself. The old mechanic is tracked by each card individually.
Let's say it's my turn, I cast a Village Ironsmith and pass.
During the opponent's turn, neither them nor I cast any spells. I have a Shock in hand, but I don't cast it because I want the werewolf to transform.
Now, it's my turn again. During the upkeep the Ironsmith transforms into Ironfang. Then, during my main phase I cast Breakneck Rider. He doesn't enter as Neck Breaker. And I still won't cast Shock, because then it would be a second spell and my Ironfang would return to Ironsmith!
Now let's use the new cards.
During my turn, I cast a Kessig Naturalist. It is the first card to care about night/day this game, so it becomes day. I then pass.
During the opponent's turn, they don't cast any spells. I cast a Play with Fire on them safely.
Now, it's my turn again, and it becomes night. Naturalist immediately transforms into its nightbound side. I then cast a Harvesttide Infiltrator, and it does enter the battlefield on its nightbound side!