The saline distributes rapidly (within about 15 minutes) from the intravascular to the interstitial compartment. And there, it is stuck.
The cells have active pumps and the membrane is impermeable to sodium; similarly, chloride is trapped.
Because normal saline is isoosmotic with the extracellular fluid, water does not have any osmotic pressure to shift between compartments, and it distributes itself according to the proportional distribution of sodium (i.e. about 25% of it stays intravascular and 75% enters the interstitial fluid).
(This may not be entirely accurate. Because the osmolality of the extracellular fluid increases, some water undegoes a shift into the extracellular compartment. The new equilibrium point is 290.2 mOsm/L. To achieve this, a whole 25ml of water has to move up into the extracellular compartment. So, the intravascular volume increases not by 250ml, but by... 256ml. What a big difference that makes. In order to remain detached from pedantic hair-splitting, I have opted to omit this from all the further calculations.)
Plasma osmolality doesn't change much, because it has received a load of essentially isoosmolar fluid.
<span>You will notice that the osmolality of the compartments increases by 0.2 mmol/L from your maths; but the osmoreceptors dont care.</span>
