Perhaps you've had a look at the Millennium rules for neutrality. It is section 9.1.
A player has to be declared neutral for a hit that comes while being checked not to count. All aggressive movement and action against a neutral player must be stopped. It isn't spelled out, but it is left to common sense that a neutral player must be tucked back in before the neutrality is declared off. If a player is called neutral while out it in the open (which is highly unusual and should be avoided even more than otherwise, and should be done when it is the only possible way to make a fair call) then the neutral player must be placed in a safe position before being called clean. An opponent who is also caught out in the open during such a call may also be sent back to the closest cover position. At least that is the way I have done it and the way I have seen it done. Shields can be very helpful under such circumstances.
I usually try to check and keep a player clean of non-hits without calling a player neutral because the rules state that we should avoid neutral calls as much as possible, because the games are fast-paced and should be allowed to continue to flow as much as possible. But a ref who sees that a neutral call is the only way to perform a fair check should not be considered a poor ref. Sometimes failure to use a neutral call results in a poor call.
I always talk to the players as I'm approaching them. I say, "Keep playing.", "Don't get distracted", " I'm going to wipe some paint off your legs", " I need to check your marker", etc.
Does this help?
Steve