The actual rule for neutrals is here:
6) Neutrals: When an Army is moved into a Neutral system, all clans with no Units in that system receive 1 week's income from the system (similar to MA's Guerilla system). The system does not fall immediately! Instead:
6a) If no clans move any Armies into the system during the next turn, the system falls under the control of the attacking clan.
6b) If one or more clans moves at least one Army into the Neutral system during the next turn, the system becomes Disputed and combat begins as though those clans were attacking a system held by the original aggressor.
How it is interpreted thus far is that you Can move your units in and out of neutrals you have just invaded, just as long as you still have some units in the neutral at the end of the move phase. If the invading clan still has at least one unit in the neutral, and no opponent has moved any units in, then the neutral is changed to the invading clan.
It might be good to clarify this rule on the website.