If you want to have cims use the train for outside connections (like tourists) you will need a passenger train station with its track connected to the tracks that leave the map. I don't think they need a specific line to be drawn before they start arriving.
I don't suggest doing this, though, for a few reasons.
First off, tourism is never worth the investment in terms of the money you get back from it. Regardless of how many tourist attractions you place or how many train stations, airports, or harbors you build, you will never have more than a few hundred tourists come to your city each week. Each tourist also only spends a few dollars worth at most (usually closer to 1) that you can collect taxes on. Since there are so few tourists you will essentially never make up what you are spending in tourism-building upkeep. I would only suggest placing the tourism buildings for aesthetic or role-playing purposes, since they only negatively effect your city's income.
Secondly, tourist passenger trains are a bit of an issue in the game at the moment. They spawn often but with only a handful of people in them (usually <5 out of 240 seats on the train). Planes and ships have this issue as well, but trains are special in this case in that they need tracks to get around. Passenger trains spawning as often as they do can quickly clog up your outside train connections. This also blocks cargo trains on the same tracks, which can lead to abandoned commercial and industrial since they then aren't getting the goods they need.
