Because AD is different, they can only use their order to deploy, whilst HD can use their order normally.
Please stop adding 'later'. It is not in the rules. The Order is generated in the Order count step of the Tactical Phase, like all other Orders. Nothing in the English Hidden Deployment rules says that it is generated at a different time. Provide a rules quote that says it is not a Regular/Irregular Order. The exact wording is different. The 'logic' of the rule is the same.
Ok. I think I understand what you mean, and they generate that order at the same time but is only for them, the "later" is from mixing with the spanish version. Ok But that enforces what I am saying that "that order" is not their normal regular/irregular order. There is nothing in the rules that states that (they could be as in the spanish version, or just say that they don't add it but save for their own use instead of how is written). And also, what do we do if they generated more than one order (impetuous for example, is not stated as in AD)? We adapt our interpretation again so that "generate an order" would also mean to all of theirs?. Maybe is your turn to provide rules for those orders beign the same Finally, (this all is for the interaction with TA) if the trooper is not deployed (HD for lieutenants says they are not deployed so LOL activates) how can we put an irregular order beside him? Or even activate TA? But don't worry. We all know if there is faq/errata of this how will end, so now is clear to me this debate is futile
We actually have instructions on how to handle Hidden Deployed or AD Impetuous troopers, it's under the rules for Impetuous. Beyond that, the type of order a trooper generates is denoted by it's training, a Regular trooper generates a Regular Order. Hidden Deployment does not change this, how do we know? Because nothing in Hidden Deployment says that we change the type of order generated. You're adding in complications that just don't exist! Placing an Irregular Order secretly next to Cutter in your Army case is technically RAW as the rule doesn't say place the token on the board, just next to the miniature :P
I would argue that strictly RAW, the game table is the only area that is governed by the game rules. Placing active game elements outside the game area is strictly not governed by a game's rules unless specifically called out to be and you are above all else NEVER allowed to keep the order secret (the status of the order is open information, explicitly)
The rules for the Tactical Phase say that the Orders of troopers not yet on the table are kept secret. http://infinitythewiki.com/en/Start_of_the_Turn:_Tactical_Phase Undeployed Troops Troops that have yet to deploy on the table (for example, due to the Special Skill Airborne Deployment) do not contribute their Order to their Order Pool. Undeployed troops' Orders are Private Information, so their player can keep their Order Markers secret and out of sight of the opponent.
Which doesn't address the fact that you are using your gaming case as the play surface as if the trooper is deployed.
But the rules also tell me to keep the generated orders secret, so I have to secretly place the token on the board?
The game tells you to place the order next to the model when it is generated, that's the issue here and how it differs from other orders that are generated without a distinct place to put it. The model is not on the board so you can't place it next to the model.
Or you generate it secretly, then place it next to the trooper when it (and it's orders) are revealed.