Show them. :) It's always best to lead by example. Have your Non-player characters use specific references and attitudes that can be easily copied -- however clumsily at first! -- and keep on hammering them with good examples until they get the hang of it.
If and when players lapse into American-speak or other characteristics you don't want to encourage, again rely on your NPCs. Have them misunderstand, react poorly to innocent comments, and provide other negative reinforcement (tho as little as necessary) to illustrate the worst-case scenario.
As noted in other responses here, reward it when they try. Keep the rewards small at first, but specify clearly exactly how much they're getting for which comments, attitudes, and actions. Then increase the rewards in response to more and better attempts. Next thing you know you'll have started a trend... and the better players of such roles will be getting bigger and better rewards. They'll keep leading by example, taking a lot of the load off your shoulders.
Finally, find written works (if you can) that can supply both ideas and one-liners that can be used or copied by the players. Such things will vary widely by setting and culture, else I'd recommend specific examples.
Best of luck!
An effective command and control structure uses decentralized authority to give decision-making capability to those with the most facts at the appropriate level of granularity.
In modern military thinking, there is the idea of
what I call articulation* decentralized authority1, 2. Roughly speaking it's that officers are not lords and masters, but that they have a job to do, just like everyone else in the unit. As orders are passed down from higher echelons transforming from strategic to operational to tactical, every person gets the general orders and then articulates them, adding their own expertise to accomplish the stated goals. Thus, a general says "we need divisions x to accomplish mission y". His decision is articulated by his staff, creating movement orders that provide for the necessary logistics.
Every unit then gets their own, smaller, orders that describe the unit's objectives. These are then articulated by the CO of the unit to correspond with the particular strengths of that unit.
In summary, the "Leader" should set goals for her subordinates, but needs to trust their expertise in accomplishing those goals. As everyone knows the objective the Leader's job is to coordinate the different skill-sets to achieve the objective, not to tell those people how to do their jobs. In older militaries, enlisted conscript soldiers had less expertise and had to be micromanaged. (Contrast: Soviet v. American military styles. And the basis of Warrior v. Soldier)
Avoiding micromanagement and practical examples
How do we apply this in game?
First, every person in the unit should be a specialist in something.
The "leader" should be the one who gets the orders (written) and has to interpret them for her squad. Her other functions should be logistical and running political interference.
The other specialists should have useful domains depending on the squad. If people double-up, they are a team under this level of organization (useful for people who don't want to accept agency) and should focus on mutual support. A key component here is that the leader is the one who makes sure everything's in place in order for her team to do their jobs. If she's trying to do their jobs for them, something else will fall apart.
The problem with this design is that being the CO of a squad is actually quite difficult. If it's abstracted away like is done in so many RPGs, the leader then has nothing to do. It's important to find the right mix of authority and responsibility that the characters feel comfortable with.
Subordination: if a PC doesn't want to take orders, try to see where the sticking point is. If they want to accomplish their own goals in their own ways, they are violating the social contract and this isn't the game for them. If they don't want to be micromanaged, make sure the leader understands the point of articulation: the leader should point out a goal, and then let the specialist take care of that goal while she goes onto the next problem.
Being an effective leader: This is a problem best handled at the player (rather than character) level. Some players like playing with logistics and politics and strategy. Make sure they're the ones in the leader spot and then give them problems in logistics, politics, and strategy. Demote their character, for cause, if they screw up. If necessary, promote one of the other characters or ask another person in the group to roll up a new character and take a swing at the problem. It's critical that you let players know what they're in for when they're sitting in the hot seat, though. Most people don't want that level of responsibility and it's unfair to surprise them with it.
Decrease in collaboration: Make sure the leader has enough to do that she can't micromanage. Some players will want themselves to be closely managed, though, and there's not much you can do to force a player to take agency. I would suggest that this is a feature, rather than a bug. Most "collaborative" plans I've endured while gaming have gone horribly wrong.
2 I believe the "officers just have a job to do" and the differences between warrior and solider feature in Kildar by John Ringo. But I don't have a copy at hand to search through.
This reminds me of a well known author who said (paraphrased) that if they spend weeks researching it, there'll be a whole chapter on it!
So, slow it down and give them little bits to digest. Let's go with food as an example: a friendly NPC invites the PCs for a dinner party where NPC plans on impressing the local governor. Sadly, a day before the dinner the provisions get stolen/burned/whatever. So, the NPC asks the PCs for help: find me food and chefs to cook/prepare it! By the end of this short adventure, the PCs will know more about Roman food than you expected. Of course, this leads to the temple of X where some priests find that the NPC has "offended the gods" and took to humbling said NPC. This leads in to exploring religious dogma and theology as a follow up.
In addition, you can set up some mysteries that require in-world knowledge to solve. For example, knowing that a legion always travels 20 miles a day is vital in planning where the PCs need to flee from the Barbarian horde wanting to skin them alive. Another example, the guy offering to help the PCs might not take too kindly to be laughed at because he carries a wooden sword. Just make sure that your players know about those facts or can find them.
So in a nut shell: Make it small and relevant to the PCs. The players should then run wild with it.
In addition, I would look at your surroundings: music, lighting, snacks, and so on. What can you do to make this more Roman? You do have olives as snacks, right?