In your example: "He has come to see if I am okay" I would think he is still there. But you could also say: "he has come to see if I am okay several times" this week, this month, whatever. In that case it doesn't mean he is still there, it is a different use of the present perfect. The week hasn't ended yet and you are considering time until now. If you say "he came to see if I was okay", then you look back on that past moment even if it is only a few hours ago. It is in the past.

In your example: "He has come to see if I am okay" I would think he is still there. But you could also say: "he has come to see if I am okay several times" this week, this month, whatever. In that case it doesn't mean he is still there, it is a different use of the present perfect. The week hasn't ended yet and you are considering time until now. If you say "he came to see if I was okay", then you look back on that past moment, even if it is only a few hours ago. It is in the past.