Why did this end?

[Mauro]

No one had negative points, East won; so why there wasn't a continuance?

[Shirluban]

It's a case of "agari yame".

Agari yame is an optional rule allowing East player to end the game if he wins on South 4 and is first.

[Mauro]

Just to know what to do if this happens to me, do you know if on Tenhou a button pops, like for tsumo and ron?

[or2az]

No button. It's automatic. An optional rule built into the game.
As Shirluban said, and from Barts guide, page 11

Under the Agari Yame rule, if the dealer (east) wins the final hand of the game and they are
leading on points they can choose whether to play a continuance as usual (and risk losing) or
finish the game early (and ensure their victory). Some video-games will give you the option to
finish when you're in this position while others will automatically end the game for you.

From what I have read, not many Japanese rulesets allow agari yame, with 6 out of 8 common Japanese rulesets having this ending disallowed.The remaining 2 allow agari yame, as does Tenhou.
I actually thought it was more common.

Source: Simon's Riichi Site, RCR issue: Agari yame

[Gnom]

I'm not sure competitive organizations' rules are representative of what's most used... I don't remember exactly how common agari yame was in free jansous but it feels like it was pretty often allowed.

[Senechal]

Echoing that statement, other people who have went to Japan and played consistently were not bound by those statistics, which originate from hakata21.

A new set of statistics, should be aggregated, and if humanly possible, weighted against their relevance. Some of the hakata21 references have been shown to be unworthy of a reference.

[Gnom]

If someone wanted to make some stats they could use this website : http://www.jan39.com . It's a kind of jansou annuary with prices, rule sets and such. It may be difficult to automatically parse because the rules seem to be handwritten except for the most common (or maybe there's an option somewhere with a standard list, I never really used it for the rules). For example, here's the ruleset for a jansou I went to a couple of times: http://www.jan39.com/rule.php?tnp=00069

・ ラス親は順位に関係なく何着でもアガリ止めができる。(単独トップは自動的に終了)同着トップの場合はラス親が続行か終了かを選べる。