I think your observation is related to the observation that if you have a (cilindrical) glass with water and tea leaves resting on the bottom, then gentle stirring will tend to gather the tea leaves at the center of the bottom.
Here 'gentle stirring' is meant to convey that you want the rotating fluid to be as close as possible to solid body rotation
You can get actual solid body rotation when the container is itself co-rotating with the rotating fluid. In the case you are asking about the glass is not co-rotating, so the fluid layer that is in contact with the wall is slowed down due to friction.
In the case of solid body rotation every single part of the fluid is experiencing the amount of centripetal force that is required to sustain circumnavigating motion at that angular velocity.
But with the layers of fluid close to the wall slowed down the fluid level (close to the wall) cannot climb up enough to provide sufficient centripetal force. So: the top layer flows towards the outside. This pushes the fluid layer that is close to the wall down. This downward motion pushes the central columnn up.
Apparently the eggs you are using are only barely non-buoyant. Apparently the upward flow of the central column is sufficient to lift the eggs up from the bottom of the container.