Both the water and the oil are in the same phase - they are both liquid.
Gas, liquid and solid is one definition that illustrates three phases. But in a more general terms, such as within phase diagrams, phases can be subsets within gas, liquid and solid, connected to specific combinations and orientations of atoms and molecules than can separate from each other. In a loose sense, a cell has its own phase diagram with the various organelles phases within the water matrix of the cell. Like any phase diagram, these are repeatable as long as the parameters (position) on the phase diagram are the same.
Picture this system. We have oil and water with the oil floating on the water; two liquid phase system. We have a second beaker with methylene chloride and water, with the water floating on the methylene chloride. We carefully stack these three phases (oil, water and methylene chloride) with oil on top, then the water and finally methylene chloride on the bottom.
Since the oil and the methylene chloride are mutually soluble (non polar), if we shake this the three phase system will end up with two layers. But if we are careful, we can form a metastable three phase system, that will slowly attempt to form two layers since this is at lowest energy. The shaking create the activation energy for a quick change.
The cellular phase diagram is designed in this way. The innards of many protein are more hydrophobic and the surface more hydrophilic. This means the innards could mutually dissolve into each other, but the water in the middle keeps then apart in a slightly potentiated state. There is built in energy created within these metastable phases that is being partitioned by the water so it remains as a separate phase.
If we go back to water and small chemicals, say we start with our three layer system of oil, water, methylene chloride, with the water in the middle. I will inject a fourth material, which in this case is an alcohol, into the middle water phase. This will define a new water-alcohol phase on the diagram. This new phase will have an impact of the surface energy that separates the layers. The three layer system is not quite as stable.
If we go back to small molecules and protein, when we add these to water phase, there is an altering of phase separation energy. This may cause the protein to be stuck open or closed.