Firstly, is that correct?
Yes your intuitive understanding for this part of the Coriolis effect is correct.
The second part, that is, why wind in the East direction is deflected South, is a bit trickier, and involves the use of centripetal force. this is given by the equation:
$F = \frac{mv^2}{r}$
If we re-arrange the above equation, we can find $r$ in terms of $v$, and we arrive at:
$r = \frac{mv^2}{F}$
This tells us that as velocity increases, the radius required to maintain the orbit also increases.
Now let's apply this concept to winds on the Earth. If we feel no wind on the Earth, then the air in the atmosphere is travelling at the same velocity as the Earth. The Earth is naturally spinning towards the East.
In the case of an additional Eastward wind felt on the Earth, this wind has effectively increased its velocity, and therefore the above equation tells us that the radius of orbit must increase as well. Radius in this case is the distance, measured perpendicularly of the Earth's axis, between the axis and the wind.
In order for the radius to increase, the wind moves southwards, where the radius is larger.
Similarly, wind moving in the West direction, is moving in the direction opposite of that to the Earth, and therefore its velocity is decreased. Consequently this wind moves towards the North, where the radius is less.
The above image shows what happens. The wind moving East begins to expand its radius, thus moving outwards. Gravity pulls it back, and the wind moves South, in order to maintain the larger radius required for its increased velocity.
The Coriolis force is analogous to $\vec{u}$ x $\vec{Ω}$. This is the cross product between the velocity of the particle and Ω which is the angular momentum of the rotating frame with respect to the moving mass. So, for a particle moving near one of the hemispheres, the angular velocity vector is pointing upwards(normal to the Earth's surface) while for a particle moving near the other hemisphere it points downwards(again normal to the surface). In order to understand this, you just need to visualize the angular velocity vector seen by two observers, each on one hemisphere. So, if the mass in both scenarios is moving say to the center, the Force being the cross product of the velocity and the angular momentum will point to the right for the first hemisphere and left for the second hemisphere(right and left here mean with respect to an observer on that hemisphere). In both cases, if the mass moves with the same velocity in magnitude, then the force will be equal in magnitude. Also, I think that checking out the Wikipedia page for the Coriolis force will help a lot, especially with the visualization part.
(Note: the Coriolis force direction can be found with the right hand rule just like the magnetic force can be found in the same way when a charge is moving in a magnetic field)
Best Answer
The direction of deflection of the ball should be independent where the observer is. Left or right deflection is with respect to an observer facing in the direction the ball is moving.
Are you asking about a ball being thrown from the northern to the southern hemisphere? In that case the deflection would change from deflecting right to deflecting left as it crosses the equator, though near the equator the amount of deflection is minimal.