it's very simple friend! 才 always denotes to late activity, and 就 denotes some early activity. in this sentance class began at 8 o'clock but he came at 8:10. ( here he 10 minutes late so we use 才 for late) 就(jiù) sentence tells us that the event of learning was completed at the explicitly mentioned time, before the expected time. 才(cái) sentence, on the other hand, tells us that the event was completed at the explicitly mentioned time, but at the expected time, the event hadn’t been completed yet. So the 了(le) in this construction is about completion– but not with respect to the explicitly mentioned time. 就(jiù) sentence requires a 了(le) because the event is completed before the expected time arrives. 才(cái) sentence forbids a了(le) because the event isn’t completed before the expected time arrives. When you use 就 in that situation, the 了 particle is important because the speaker wants to emphasize the action has started/finished/done before a certain time (it’s not necessary to be a completed action). Only the mentioned moment is before a certain time, so the 了 particle emphasize the action “has happened”(←the 了 particle here for this reason only) . As for the 才 sentence, the speaker wants to emphasize the belated time, so the action is not important enough to add the particle 了. hope now you will understand clear.

才-is used to show that the speaker feels whatever is happening is a bit late. 八点上课，他八点十分才来。Class starts at 8 but he didn't arrive UNTIL(this is what 才 means here）8.10. 今天我去北京饭店，八点坐车，九点半才到 Today I will go to Beijing， I will get the train at 8 but I wont arrive UNTIL(才） 9. (I have used future tense as this sentence has been written in a way that the tense is not clear) 了 is not used as 了 indicates a change of state or a completed action and that does not apply to these sentences. In fact I don't recall seeing or using a sentence with 才 and 了 together。

八点上课，他八点十分才来。 今天我去北京饭店，八点坐车，九点半才到 For your question, we don't use 才 with 了. We use them singly. 才, here means so late and a emphasis on his late in the sentence. Sometimes even shows somebody's complaint for the late. eg: 你怎么才来. Why do you come so late.

It depends on the context. 1. If there is a scheduled time but someone is late, 才 implies a tone of complainsand it means unexpectedly and unhappily. E.g. 约了你8点钟，怎么你8点半才来啊？ 2. It also can be used to respond or explain for how long you have been somewhere or done something. It means "just now" or "very recently", or "newly start doing sth". The time or degree to modify the sentence must be slight. E.g. 我才到这里没多久。 他才吃了几口饭就饱了。 3. It can also be used to emphsize the tone of sentence. It can make something wrong clear and correct. But it really depends and need experiences. E.g. 我才是她男朋友( Implies that someone mistook others as her boyfriend) 我才不要去那里（Implies that someone mistook that "I" would love to go there.） To be added.

it seems there is no sentence that use both 才 and 了, if 才means late or just happened, you say “你怎么这会儿才到”，“都（已经）中午了，你才吃早饭”，“已经撞车了，你才踩刹车” and so on