Is seeing the person who married another woman after performing Istikhara a result of it, or just a coincidence?

If you seek Allah's guidance concerning a matter, proceed with it. If it becomes easy for you and your heart is at ease, then it is good for you. Otherwise, turn away from it. It is not a condition that you see a dream for this. So, if you seek guidance concerning a suitor and your heart is at ease, accept him. If the matter becomes easy, it is a sign of good. But if your soul feels constricted, or the matter becomes difficult, or he turns away, then there is no good in it for you. And your seeking of guidance has no relation to seeing a third person who is married.