Why it exists. To say that one action happens right after another: verb 1 + 了le, then 就jiù + verb 2. Zhou Qing in Text 4: 音乐会结束了你们就给我打电话yīnyuèhuì jiéshùle nǐmen jiù gěi wǒ dǎ diànhuà.

Personverb 1了(object)就verb 2

+他每天起了床就喝一杯咖啡。Tā měi tiān qǐle chuáng jiù hē yì bēi kāfēi.Every day he has a coffee as soon as he gets up.

+你到了宾馆就给我打电话。Nǐ dàole bīnguǎn jiù gěi wǒ dǎ diànhuà.Call me as soon as you get to the hotel.

+她收到了邮件就给我打电话了。Tā shōudàole yóujiàn jiù gěi wǒ dǎ diànhuà le.She called me as soon as she got the email.

+我们看了电影就去吃饭吧。Wǒmen kànle diànyǐng jiù qù chī fàn ba.Let's go and eat right after the film.

Key points

了le comes after verb 1, usually before its object: 起了床qǐle chuáng, 看了电影kànle diànyǐng. In speech you also hear 到家了就……dào jiā le jiù….
Already happened? Add another 了le at the end: 她收到了邮件就给我打电话了tā shōudàole yóujiàn jiù gěi wǒ dǎ diànhuà le. For plans, habits and requests there is no 了le at the end: 你到了就给我打电话nǐ dàole jiù gěi wǒ dǎ diànhuà.
就jiù or 才cái? 就jiù = right away. 才cái = only then, later than expected (Lesson 3): 他看完了书才睡觉tā kànwánle shū cái shuìjiào "he didn't go to bed until he'd finished his book".
Two people? 就jiù goes after the second person, right before verb 2: 你到了我就去接你nǐ dàole wǒ jiù qù jiē nǐ.

Common mistakes那天我到了北京就给妈妈打电话。 → 那天我到了北京就给妈妈打电话了。Nà tiān wǒ dàole Běijīng jiù gěi māma dǎ diànhuà le. It already happened, so add 了le at the end.
你到了宾馆就给我打电话了。 → 你到了宾馆就给我打电话。Nǐ dàole bīnguǎn jiù gěi wǒ dǎ diànhuà. A request: no 了le at the end.
你到了楼下就我下去接你。 → 你到了楼下我就下去接你。Nǐ dàole lóu xià wǒ jiù xiàqu jiē nǐ. With a second person, 就jiù goes after that person, right before the verb.