It is, but the intersection point doesn't track the station. When you push an object retrograde (i.e. throw it out the back), two important things happen. One, you make it spend more time closer to Earth than it was spending before, meaning extra drag, which lowers that orbit's closest point to your orbit, ever so slightly. Two, objects in lower orbits move faster, contributing to drag, but more importantly, meaning that once you do one full orbit, the object will be somewhere else. It may still roughly intersect your orbit, but you won't be there when it does. Combining these two factors, you can give your object enough of a push that the two orbits stop intersecting before there's any risk of collision.

The eccentric orbit is the transfer orbit but yes, you need two thrusts to go from one circular orbit to another.