the players that pop up in your encounter screen are generally there because of random encounters, if they had followed you they would appear the same second you appear in an encounter map... and follow John Ryder's advice.
also, when you log off while you are in a city or mine (or even somewhere rondom in the wasteland), it takes 3 more minutes for your char to disappear from sight. that means even if you have logged off the game, other players can still kill you or steal from you, or plant a dynamite in your pocket for 3 more minutes and due to the fact that you don't see that coming, you cant run from them, and you are more vulnerable than ever... so, you better log off when you are in the world map screen or in your tent.