Tempus is EN3. I will now present proof.
Myth was the first generation of EN-only talents from Hololive, and their debuts came off the back of HoloJP management. Auditions for HoloEN were initially tweeted out by HoloJP twitter, and the JP side management of Hololive had a lot of input in how the HoloEN branch would be shaped and perceived.
Hololive EN debuts were also extensively advertised, and the plans for an EN branch was well known among the JP Holos. Coco even made an advertisement for their auditions (
https://youtu.be/1I43s0oFbbk).
The newly recruited HoloEN managers also worked closely with their JP counterparts.
In comparison, the first generation of EN-only talents from Holostars (Tempus) debuts did not involve StarsJP management at all (Shinove included).
Oga confirmed that neither StarsJP management nor the JP Stars themselves were aware that they (HoloStars JP) were about to get an EN branch (
https://youtu.be/-QKRhLSnAwY).
In stark contrast, Sana and several other members confirmed that they were talking to the Tempus members and giving them help and encouragement before debut (
https://youtu.be/5AAk6aNc8qE) and even getting tech support from Vesper. HololiveEN talents and management were aware of the upcoming "HoloStars EN" debuts, but not anyone from "Holostars JP".
In practice, what this means is that Tempus' direct senpais are Hololive EN. They consider StarsJP as senpais as well, but in the same way they consider HoloJP as senpai. A distant second to Hololive EN.
Tempus' scouting, recruitment, training, debuts etc. were all handled by a section of HoloEN management which has been split into managing StarsEN (or new recruits who were trained by HoloEN managers). As far as we know, there has been zero involvement or input from Shinove or anyone else from Holostars JP management in how "their" supposed EN branch should be handled.
This is why there's very little bureaucratic friction with respect to HoloEN and StarsEN collabs. Tempus is a "different branch" from Hololive EN in name only (then again, there are no Generation names in HoloEN, remember?), they're practically managed by mostly the same people who are managing HoloEN.
And so, in all but name, Tempus is the 3rd Generation of Hololive English.
