I am just trying my second mission after the tutorial. First one went fine (I don't think it's even past day one yet), I snuck around with two agents and pretty much cleared the map with take-downs (though I only found one loot and one secret).

Second map, it seems to start combat after, like, maybe two-three turns? I went the opposite way on my second try, and I was still on the street trying to recon in both cases when it went "you're in combat now.".

The mission muttered something about "you don't have much time" or something - is this a mission where you just automatically go into combat (If so, I'mma quit and go to an earlier save, my first experiment into doing it as a shooting map demonstrated the impracticality of trying to do it thei early in the game).

Or is something else doing it? I know enemy agents see through your disguise, and though the agent showed up the first time (so I thought I must have just unluckily wandered into sight), the second time I was nowhere near that location - so unless the enemy agent starts making a beeline for my location disregarding actual visibility, I can't see how they could have done that.

Niether agent is ID compromised. (I learned the hard way that the little timer that shows up at a suspicious location is NOT a timer for my guy to do their mission, it's the enmy one. Obvious in hindsight, but it was late Christmas Day and it wasn't instanlty obvious to me...!)

Edit: It says "alarm raised by force majaure" which, on the second time when I googled it, would seem to suggest it is an automatic switch yes?

Yes. Force Majeur means you didn't do anything wrong and a mole or some other method allowed the enemy to know you were on sight. That happens in plot missions more often but will occasionally occur in a normal mission. If it was not a plot mission you can reload a save before the mission and restart and it will generate a new layout that may change the conditions.