It means exactly what it says. If there are one or more people who have come from somewhere else, then it describes the first man to have arrived.
It doesn't necessarily mean that he has just arrived.
If the event were being commentated on, the sentence could be spoken when the man appears. Many hours later, especially if no other man has arrived, the sentence could be spoken again—although, in that case, it would probably be more common (although not essential) to say he is still the first man to arrive here.
In another scenario, consider a fantasy story involving a quest that has always been completed by women:
Although many women have done so, he is the first man to complete the quest.
He could have completed the quest many years ago, but you could still use the present tense while he is alive. (If he were to die, then the past tense would need to be used.)
Just because it happened at some point in the past doesn't mean that you have to use the past tense when you are talking about a still-existing quality of a person. If something is still true, or if it's a general truth, the present tense can be used in addition to the past tense.