用He hasn't come yet.这样比较符合语境~~
并且你两句的don't都要改为doesn't，因为he ，要用第三人称单数~
Both statements do not contain any grammatical errors.
However, there are too few descriptions of the situations. Thus, even though both of them are correct, their meanings may not be what you want.
He hasn't come here yet
He didn't come
对啊！
无什么错啊！谁说yet 一定是用在现在完成时啊！
他还没有来 He don't come here yet. 不对，有yet应该用现在完成时 应该是 He hasn’t come here yet
他没有来 He don't come here. 不对，应该是 He didn’t come here
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