八点上课，他八点半就来了。Firstly, this sentence is wrong in Chinese, it would right if it is written in 八点上课，他七点半就来了。 In this sentence, 就&才 means he comes earlier. 八点上课，他八点十分才来。才means he comes late. 昨天我去北京饭店，八点坐车，八点半就到了。 到 means the train was very fast and you arrived in a short time. 今天我去北京饭店， 八点坐车，九点半才到。才means the train was very slow and you arrived late.

It is a little difficult to explain your comment but I will try my best. If 就 appears together with 了。It it a structure to express that has been finished. And 才 always be used alone.

八点上课，他把点半就来了。 He arrived before schedule. 八点上课，他八点十分才来。 He didn't get there until after schedule. That is exactly what those two words imply.