You have to use waypoints to ensure that a line is always using a different track than the one selected by the game by default. I do think that the game itself tries to spread out lines in a station as much as possible, but it cannot do this work if your tracks don’t support it.
Waypoints can be either the explicitly given waypoint sign, or any signal (no matter from which direction you approach it), or one of the plenty waypoint mods available online. You’d arrange it in the line route just like a station, i.e. from station A to the waypoint to station B. Note that trains don’t reverse at waypoints, only at stations.