There are several ways to move particle along splines. Which of them you need depends on how the particles should behave.
1. Stick exactly to the spline
2. Move freely within a given distance to the spline
3. Move along the complete length of the spline in the particle lifetime
4. Keep current speed and just change direction to follow the spline
Of course there are many more options and combinations but these four should give you an idea on what can be done.
Using points to steer particles
In this example PPosition Follow is used to make particles follow different points of a spline over time. An iterator will go through all points of a spline (or any other object with points) and use the age of the particle to determine which point it should follow. This is done by calculating a quotient of the age and the lifetime and mapping this on the number of points. The older the particle the higher the number of the point it follows.
You can also use the Spline node instead of the Point node for this, it will give a smoother movement and allows for the use of parametric splines.
Scenefile (C4D 57 KB) Movie (QT 1060 KB)
Using points to steer particles with variation
This is a slightly different setup then the one before. Random values are used to vary the spring speed of PPositionFollow to achieve a more natural looking movement.
Scenefile (C4D 60 KB) Movie (QT 1498 KB)
Change Direction to follow spline
This example is created using the same technique as the "TP Follow Spline" preset that comes with CINEMA. The idea behind it is to subdivide a spline in a given number of parts and then control particles by this. If a particle comes within the set range it will align it's movement along the alignment of this part of the spline and follow it. The higher the number of parts the more precise the movement, but also the slower the calculation.
Scenefile (C4D 80 KB) Movie (QT 530 KB)