Collected and elaborated info from the chat with the OP:
To summarize the osmolality and tonicity difference, elaborated in the below link:
- Osmolality takes into account all solutes.
- Tonicity excludes solutes able to pass the semipermeable membrane.
So isotonic solutions need not to have the same osmolality.
The osmotic pressure is caused by decreased water activity, what does not depend on if solute is or is not able to pass the membrane. By other words, osmotic pressure and related osmolality is property of solvent, not solutes, similarly as kryoscopic and ebulioscopic effects, all belonging to the class of colligative properties( depending on solute molality, but not on solute nature )
Primary is osmolality and osmotic pressure difference it causes. The difference then causes water osmotic flow.
When the osmolality is getting about balanced, then there is progressively coming into the play the difference in tonicity.
The same osmolality but higher tonicity means there is lower osmolality and therefore indirectly concentration of permeable solutes. This means there is concentration gradient powering the diffusion flow toward more tonic side. It is taking water with it, keeping osmolality balanced.
As result, volume of more tonic side increases even with the same osmolality.
At certain circumstances, the residual osmotic pressure may be compensated by the permeable solute concentration gradient, keeping status quo.