Tramlining is not caused by any geometry being wrong, although I'm sure this can worsen the effects. It's natural for all cars/tyres...
Tranlining is caused by "camber thrust", which is the increase in lateral (sideways) force the tyre is tilted relative to the road surface. As the road surface dips into a grove shape, it effectively puts the tyre or at least part of the tyre onto a slant, which generates camber thrust and the tyre will try to "climb up" the grove.
The reason goodyears or other performance tyres may tend to tramline more is because they have the ability to generate more lateral force because they are softer compounds. The increased grip means an increased tendency to tramline.
Sorry, I don't know how being directional or not would affect it, but its might be a fair generalisation to say that a directional tyre is probably a performance tyre and therefore more affected for the reason above.
Also factors are the weight of the car and the tyre width, and the rest of the geometry I suppose...
Motorcycles corner partly by expoliting this phenomenon, you can see in the second photo I've attached that he has the front wheel straight. I found a quote in Milliken that is helpful:
"The lateral force generated in the linear (small angle) range by one degree of slip angle is greater than that created by one degree of camber. For traditional bias tires the cornering stiffness generated by one degree of slip angle is generally five to six times greater than the camber stiffness."
Or to put it another way: he has to lean over at an angle 6 times greater than if he were to turn the handlebars in order to go in the same turning circle.
Sorry... got a bit carried away on this.
Hope that helps!
Alfapash: Having the tops of the wheels pointing in might be the normal camber... let us know what they say and take a photo if possible?