As is commonly known, most of the game's systems are tied to a 'cycle' of 51 'ticks' (small increments in sprite positions observable when running at slowest speed) and that there are 16 such cycles in a game month. On a particular tick in each cycle all production figures (percent complete) are updated. On a (different) particular tick in each cycle all cartpushers who are ready to spawn will do so. I had noticed that fire marshalls and architects spawn 2 ticks later than most walkers, and I believed (wrongly) that policemen spawned 17 ticks later.

I became puzzled when I was trying to synchronize two fire marshals and couldn't get them to spawn on the same 'tick', so I investigated (being one for noseying around in every corner).

In Brugle's Random walker start and finish points he describes the normal starting points for 'common' random walkers. The basic rule is that they spawn on the first non-roadblocked squarely adjacent tile encountered when starting NE of the northern tile and rotating clockwise. Brugle then goes on to describe some exceptions to this rule.

I have not looked at entertainers nor temple complexes, but in fact all other buildings observe this rule, and all walkers spawn on the same tick (actually, I'd better say 'most' ). What we have with architects, fire marshals, policemen, magistrates and tax collectors is a class of walker which spawns invisibly, then spends 2 ticks determining what to do next (which explains why an architect is often observed to spawn 2 ticks behind other walkers). You might be able to detect his presence by right-clicking in the vicinity of the building, or by holding a (unplaced) plaza tile over the road.

But that is not the end of the story. He then walks, still invisible, to the building's destination tile (though obviously not if he is already standing on it), which may be roadblocked. Only then do they cast off their veil and start a visible walk. Thus according to the configuration, the actual appearance of one of these walkers is delayed by 2, 17, 32 or 47 'ticks' relative to other (common) walkers.

Fire marshals and architects are a bit different. Instead of heading for the destination square they head instead for the square that they would have started on if it had not been roadblocked (I suspect something was changed here - if marshals and architects behaved like the other 'invisible' spawners they would start from the same tiles that their C3 equivalents do). But they still need an unblocked tile to start from.

Brugle did not deal with workcamps (because they are not random walkers) but laborers also exhibit this behaviour. They spawn invisibly at the same time as 'normal' walkers but appear 2 to 47 'ticks' later depending on whether they have to walk to a destination square first. Consider the following:

In the left diagram (north is up-left) the laborer appears on the plaza tile, but actually spawns on the adjacent road tile. He appears 17 'ticks' after spawning. In the diagram on the right, he still appears on the plaza tile but delays by 15 'ticks' because the roadbloack forces him to spawn invisibly one tile further away from his eventual starting point. He appears 32 'ticks' after spawning and thus arrives at his job a little later. It's a trivial point, but in the case of a floodplain farm, all depending on timing, this may lose you one production cycle on some farms, which may lose a percentage point (8 units of product for each farm affected).

Here's another diagram:

Here the laborer spawns invisibly on the plaza tile on the horizontal road, but walks to the plaza tile on the vertical road before becoming vivible. He does so in a straight line, going through the building itself, and so takes three tiles of travel to get there. If the building were to emit a labor seeker simultaneously, the laborer would appear 47 ticks 'late'

Note that for all purposes I can think of (default walk lengths, maximum distances workcamp to farm, etc) it is the tile on which the walker becomes visible that is relevant, not the tile on which he first spawns. The only effect is to delay the appearance of the walker.