翻译为委托制作是比较准确的，因为commission （动词）就是授权制作的意思，请看the free dictionary 的释义：a. To grant authority for (something to be made or done); 即授权把某事完成。

    看来你对commission和from习惯搭配的用法还不太熟悉。from 表示被授权完成某事的实施者的来源。请看外媒例句：

1. The housing blocks were commissioned from architects who had previously won FAD design prizes . 这些住宅区被（某方）授权由过去获得FAD设计奖的建筑师完成。

2. A plan for this was commissioned from an architect called Bruce in the fifties.  这个计划被（某方）授权由一个50多岁的名叫Bruce的建筑师完成。

你的问题句，可以有以下几种改写, 为了方便，我仅简单写个框架：

1. The magazine commissioned the architects to design and build the Case Study Houses. 

2. The architects were commissioned (by the magazine) to design  and build the Case Study Houses.

3. The Case Study Houses were commissioned from the architects.

4. The magazine commissioned the Case Study Houses from the architects. 

以上写法都是可以的。

    你的这句改写“That talented modern architects were commissioned the “Case Study Houses” by California Art &Architecture magazine  between 1945 and 1962 were是错误的。”  英语不说sb is commissioned sth by sb. 可以说sb is commissioned by sb to do sth.