Sometimes it helps to break the mechanic down to it's simplest form. Mushroom wars is a simple kind of 4x game, where you can spend your soldiers to upgrade buildings, or attack to take over new buildings. Upgrading buildings important for the long run (which in Mushroom wars is just a couple minutes), but it weakens you for a short time. This is fine unless the other player is attacking you, or if the other player has left themselves weak and vulnerable to an attack. The more abstract setting allows the designers to simply focus on the mechanics of military vs economy, without worrying about the realism of populations growing or dying.

If you want something more robust, it could be built from a core mechanic like this that lets you see very clearly how the short term and long term goals play off each other.

Real Time, so it's pretty far off from Civilization. But it's 4x. You expand across the map, increase your production capabilities, change your tech a bit, and attack your opponents. Understanding how the 4x elements work in something so simple may help to make them work in something more complex.

For your more specific question, I'm not quite sure what you're doing with the population. In Civilization, making military never affects your population directly (although the focus on production rather than food limits your population growth). Damaging a city occasionally damages a population, but it's infrequent enough that it doesn't match the population growth that cities have all the time. How is your game using population in combat that's becoming a challenge?

What I mean by time compression, is the balance within any given turn to provide meaningful interaction with elements that are clearly short and long-term.

For example, it is expected at the end of a given turn that the population can grow organically which, for most species we know, takes a matter of months.
Likewise, within the same turn, we're expected to demonstrate progress in battles, which certainly don't take nearly as long to perform, especially if the game focuses on Tactical Elements.

One of my favourite old games from the 16-bit era, Deuteros, had an interesting time mechanic. It was kind of a 4X game, not quite in the modern sense, but may be relevant to this.

It essentially simulated real-time, but allowed the player to skip ahead by an hour or a day at a time. Most events in the game occurred on a period of days or weeks - building a new ship would be a two week job, for example. If nothing else happened in the intervening period the player could happily skip all those days and the ship would be built almost 'instantly.' If something happened in the intervening period, especially something that required real-time attention like an unexpected attack, then the time skipping would stop and you would play through the relevant events in real-time. Assuming you survived the attack you could then go back to skipping days until the ship is finished. Usually you would have lots of things going on at once over multiple time scales, especially late in the game, so in practice you never skipped ahead by very much at the accelerated rate. But early in the game it was an elegant way to speed through things like "build my first mining ship and fly to the asteroids" which takes 22 days or whatever.

Of course, this wasn't just doing time acceleration and really simulating every second in between. As Krypt0n suggests, skipping a day would update the game by an aggregate effect over that period. In most cases like population growth, building a ship, or flying to a planet, the skipped time can either be solved in closed form or at least approximated over the skipped period well enough that the player would never know the difference.

TL:DR - I guess the point is that your game-time events could be to real-world scale as long as you can accelerate through the times where nothing happens.

How do you (would you) as a designer resolve this issue to keep the content balanced between high-level strategic and actual tactical implications?

it all depends on where you want your game to fall on the scale of "contrived BS vs ultra realism". too hokey, and it breaks immersion. OTOH, ultra realistic might not be a lot of fun.

time scale problems have always been an issue in strategic games - unrealistically short building construction times in RTS's being a classic example.

as near as i can tell, every 4x i've played from MOO on has had to "bend the rules" a bit. some do it better than others.

start with realistic and see how fun it is. it may not work at all, like AOE etc with no advancing to the next age - probably more realistic, but probably less fun too.

then bend the rules as needed to make it sufficiently fun, without becoming too contrived.

Do you bother explaining this to the player, or do you just 'go with it'?

the trick is to make any bending of the rules sufficiently un-noticeable as to not require any explanation. if you have to explain it, you're already breaking immersion. remember its a 4x, you get to write the rules of the game universe, unless its some sort of historical thing like a 4x about European colonization. So making it believable in the context of your game universe should be a little easier than making it believable in the context of the real world.

Once upon a time (before Acharis started turning this into a design method)

How do you (would you) as a designer resolve this issue to keep the content balanced between high-level strategic and actual tactical implications?

Do you bother explaining this to the player, or do you just 'go with it'?

I feel the cure might be worse than the disease in this case, so I would just let it go. Games are not real life, the player knows it. It must be consistent within its own rules (consistent world) but not necessarily with our world (actually it should not in most cases). I found out that ignoring some issues/realism might be a HUGE benefit to the playability, so I always consider the "ignore it" option :)

My tricks:

- focus on one side of the timescale only (like no tactics only strategic level)

- split turns (big) and then subturns (phases) which occurs on needed basis, so sometimes you have these phases and sometimes not (a concept, haven't used it yet)

- don't use any timescale and name everything "turns", like in my current in dev game the intro says "10,000 turns ago..." also imperial governors have their age listed in turns not years. So, it's a bit of "breaking the 4th wall", but also I have a more freedom since I never said that a turn is one year. Of course it depens on the game's mood, in mine it's humouristic/cartoon like so it fits, I would not use it for all games.

- ignore and move on (my favourite, typically the most elegant solution :D)