yes, you have to make room for the liquid you are going to add. So withdraw the same amount of air from the vial that you plan to put in. Otherwise, when you add liquid, the extra pressure will squirt it back out of the hole in the rubber stopper.
When you are removing liquid, first add the amount of air equal to the amount you plan to remove. Otherwise, it is very difficult to withdraw the liquid. It will feel like there is a lot of suction and the liquid will keep wanting to withdraw back into the bottle. If you have remembered to add the air, the syringe will almost fill itself when you take some out.
Do this with all three bottles: HCG vial, sterile vial, bac water vial.