你的理解还是对的！

具体分析：I didn’t phone till four o’clock in the hope that you’d be finished.

in the hope是介词短语，修饰谓语动词phone，作目的状语。意为“怀有希望”。

that you’d be finished是hope的同位语，进一步解释说明hope的内容。

从更好理解句子的角度，可以把“in the hope that +陈述句”看作一个固定句式，作目的状语。此外，in the hope可以用hope的现在分词替换，而作用不变：hoping that...

翻译：我到四点才打电话，希望你会完成任务的。

又如：

I went there in the hope that I might see her. 我抱着或许可以看到她的希望而到那里。

I called in the hope that she was at home. 我是抱着她在家的希望打电话的。

You always live in the hope that if you do your job well, justice will prevail. 人总会抱着这样的希望,只要工作干得好, 你是会得到公正对待的。

They intermingled with the crowd in the hope that their pursuers would lose sight of them. 他们混在人群中,想让追捕他们的人再也找不着。