Make sure the hose from the expansion tank to the overflow bottle is Airtight to the bottom of the overflow bottle and the Radiator cap has a good seal on the Expansion tank filler neck.
When the engine heats up, the coolant expands.
It initially pushes the air out of the expansion tank into the overflow bottle followed by whatever fluid needs to go also.
This happens once the pressure in the radiator reaches the Caps rated pressure, Typically 18psi.
The expansion of the coolant is Not trivial.
One Gallon of 50% Ethylene Glycol Coolant will expand 4.25 ounces going from 70°F to 220°F.
The expansion of the rubber radiator hose will absorb some of the volume but a few ounces will transfer back and forth to the overflow bottle.
When the engine cools down, the coolant contracts and pulls the fluid from the overflow bottle back into the expansion tank, keeping it 100% filled to the brim with no air whatsoever.
Unless the hose from the expansion tank to the bottom of the Overflow bottle is 100% airtight and the radiator cap is perfectly sealed, air will be pulled back instead of fluid and the expansion tank will not be refilled.
If this is a newly refilled radiator, it might take a few thermal cycles for all the air to get purged and the radiator to fill completely.
Refill the overflow bottle as needed so it does not become empty.