Instead of If[t < 5, Red, Green], it could be Piecewise[{{Red, t < 5}, {Green, 5 <= t <= 10}, {Blue, t > 10}}] .
ParametricPlot3D[{Sin[t], Cos[t], t/3}, {t, 0, 15},
ColorFunctionScaling -> False,
ColorFunction ->
Function[{x, y, z, t},
Piecewise[{{Red, t < 5}, {Green, 5 <= t <= 10}, {Blue, t > 10}}]]]
