すると details

Examples

and then; whereupon — the next thing happened straight away, unbidden

玄関げんかんのドアを開あけた。すると、知しらない猫ねこが飛とび出だしてきた。

genkan no doa o aketa. suruto, shiranai neko ga tobidashite kita.

I opened the front door. Whereupon a cat I'd never seen came flying out. neutral

呼よび鈴りんを鳴ならしたんだ。すると、中なかから知しらない人ひとが出でてきてさ。

yobirin o narashita n da. suruto, naka kara shiranai hito ga dete kite sa.

I rang the bell. And then some stranger came out from inside. casual

案内あんないのとおりに画面がめんの下したのボタンを押おしました。すると、確認かくにんの画面がめんが表示ひょうじされました。

annai no toori ni gamen no shita no botan o oshimashita. suruto, kakunin no gamen ga hyouji saremashita.

I pressed the button at the bottom of the screen as instructed. A confirmation screen then appeared. neutral

so that means; then — the speaker works out what the other person's words come to

すると、明日あしたの集あつまりには来こられないということですね。

suruto, ashita no atsumari ni wa korarenai to iu koto desu ne.

So what you're saying is you can't make tomorrow's gathering. neutral

それで
それで claims the previous sentence CAUSED what follows, and what follows is often the speaker's own doing; すると claims only that the next thing came immediately and was not the teller's own doing, which is why a surprise lands naturally after すると and reads oddly after それで.
たら
〜たら holds both halves in ONE sentence and needs a predicate inside it to hang off (窓まどを開あけたら、雨あめだった); すると needs that first half already closed with a full stop, which is what lets a storyteller pause before the surprise.
そこで
Both pick up a sentence already closed with a full stop, and they split what may follow — すると reports what the teller then saw happen, somebody else's deliberate move included (事情じじょうを説明せつめいした。すると、彼女かのじょは黙だまって財布さいふを出だした), while そこで introduces the move made in response, so a surprise after そこで and the teller's OWN chosen next step after すると both misfire.

と
The same と, one word apart — inside a sentence 押おすと開ひらく hangs the と on a dictionary verb and states a condition; すると is that と welded onto する and standing alone, pointing back at the previous sentence, so there is no condition being set and nothing after it is a rule.