Water in a glass Consider water in a glass and glass is held in hand. Hand is steady. Surface of water will be flat.
Now if the hand is given angular motion in a horizontal plane (w.r.t. floor) i.e. glass is moved along an arc of horizontal circle, surface of water will not be flat.
But the same glass of water when it is stationary (on, say, table or floor), the surface of water is flat, even though earth is in circular motion (daily rotational motion) about its axis of rotation.
Earth is non-inertial frame of reference from glass point of view.
Hand in circular motion is also non-inertial frame of reference from glass point of view.
Then why the difference? Why surface of water in stationary glass is flat?
 A: Earth is rotating at an angular velocity of 15°/mean solar hour, i.e 360°/24 hour. Now the experiment you are doing, there the angular velocity of your hand is much more than that, say about 360°/2 sec. From here you can compare how fast you are doing that. If you do it with 15°/hour the surface to water will remain flat.
A: You are correct in that the surface of the Earth is not an inertial frame of reference (strictly speaking). Objects at the Earth's surface are indeed subject to inertial effects. For example Coriolis force, centrifugal force etc.
But because the earth's rotation is very slow and the earth is very large, for small-scale phenomena, like the experiment you mentioned, we can in practically consider the surface of the earth to be an inertial frame of reference.  This is why the water in your glass appears stationary and flat.
But if we were to consider large scale phenomena, like cyclones, then the earth's rotation becomes relevant, and we must consider it to be a non-inertial frame of reference where we need to factor in inertial forces. So if we made your cup of water to be about the size of a huge dam, the Coriolis force will have an affect on the density flow of the water.
Also, for detailed information on the Coriolis force, see this.
