Those will be tourists then, since you always have a clear indicator on the map as to their location and numbers. Really, all you have to worry about is not letting too many tourists dwell at a station\stop at once. Bigger and better stations\stops can handle larger amounts of waiting tourists before said tourists experience any dissatisfaction, since it is the number of tourists concurrently waiting at a station\stop which leads to any dissatisfaction.
In this scenario, since there is only one Tourist Attraction on the map, tourists will want to go back home after visiting the local Castle. So, if you had sufficient transportation infrastructure to bring them here in the first place then you’ll likely have sufficient transportation infrastructure to take them back where they want to go. The number of tourists that came inbound from the North or South is how many will want to go back Northwards or Southwards.
In scenarios with multiple tourist attractions hooked into your transportation network they’ll often try to visit multiple tourist attractions before heading back home off-map though. No need to fret too much about any dissatisfaction as long as you can either; adequately hold hundreds of tourists at a station\stop for a while, or transport them away promptly. For example, tourists will wait overnight at a station\stop without issue as long as their numbers don’t surpass the station\stop’s overcrowding threshold.
Easier to envisage demand for construction materials in a different manner. Stations\stops which see high passenger traffic are areas that will see high rates of development and subsequently high demand for materials. Underdeveloped areas around busy stations\stops typically more so than already well developed areas, but developed areas can undergo redevelopment.
Not at a quick glance, the total number of daily tourists wanting to travel onto the map (into the region) is fairly obfuscated. With the rather leisurely pacing of the game though, due to the way it progresses via 24-hour days and the various game speed options, you can follow your tourist route vehicles around the map between the hours of 6am-12pm to get a feeling\approximation for daily tourist supply.
Simplest step is to check whether your vehicles are operating at maximum capacity between 7am-10am, the busiest period for inbound tourist travel. If they are regularly full then expand passenger capacity using the options available to you, longer trains or more trains. There’s a pool of tourists generated for each neighbouring off-map town\city between 6am-12pm, so it should be fairly obvious when you’ve begun oversaturating a tourist route if vehicles in the prime 7am-10am timeslot are individually transporting less tourists than before.
Simplest step is to start out small, observe for a few game days, and expand if necessary. If using one vehicle constantly leads to it running fully loaded tourists and passengers then add another to the route. Usually about an hour’s interval between departure times is my starting rule of thumb. Though, particularly busy routes might be able to sustain smaller intervals between vehicles arrivals\departures; such as 30-minute or 15-minute intervals.