So it changes the meaning depending on where it is

他起床就八点钟了 - He got up at 8 (late)

他八点钟就起床 - He got up at 8 (early)

他起床才八点钟 - He got up at 8 (early)

他八点钟才起床 - He got up at 8 (late) 

时间 + 才 --->>比指定的时间晚 (later than expected)
才+ 时间 --->> 比指定的时间早(earlier than expected)

Normally we can tell by accent.  Natives put different accent on different letters . For example 

我八点钟才起床  we would elongate the letter "八", so people could focus on the letter “八”and understand that it's later than expected.

现在才八点种 we elongate the letter"才" so people could focus on the letter “才” and understand it's earlier than expected.

To figue out and remember the rule of position,  it helps for sure. But I think meaning and content is much more important. Actually it's not where we put it that matter. It's because these two "才" have different meanings, like polysemy in English. 

我8点才起床。才：begin to....

现在才8点。才：merely, only 

我8点钟才起床（不到8点绝对不起床, 7:59也不起床）

现在才8点钟（eg: I get up at 8:30 every morning. But today I woke up at 8:00. So I think it's  just at 8 o'clock, I don't want to get up until 8:30.）然后我就会说我8点半才起床