To quote a very good old cartoon...
QUOTE (Some character from Two Stupid Dogs)
Awww isn't that cute....BUT IT'S WRONG!
no seriously you are of course placing the pieces incorrectly together. As you obviously have noticed FinalSun_DTA uses actual set pieces for it's rivers and they run together similarly to how the dirt roads of normal TS do. As in there are 8 direction with tile sets that allow for change in direction. However, here you lack a Marble Madness mode to show that this piece can run into that piece without overlapping any sections and not leave any sections un-covered.
I would post some screenshots of my own showing correct placements and what not but I can't be bothered to do that right now. All i can say is that just as long as you don't see any hard straight edges of anything then it should be good.
DTA maps take a lot of effort and planning to do. And you have to do one section at a time. Like you can't place cliff A and then place cliff B a ways away and expect to connect them. Thus you have to work start from finish on sections like cliffs and rivers otherwise you will likely find yourself redoing parts of the map as you couldn't connect areas because of the limited tile set types. Which is why I haven't finished a map for DTA yet. I have messed around with it a good bit though.