If the hex is yours, the planet is yours. The fact that it is 'neutral' on the attack screen is irrelevant. For all practical purposes, you own the planet, since you own the hex. You can use planerary facilities (shipyard etc), you get repairs, and so on.
In fact, its even better that the planet is neutral; you can keep attacking it, for more pp, free and automatic repairs immediately after battle, and a DV boost!
-suleo