In version 13.0 there were some issues with vertex colors for tubes which has been fixed in 13.1.

However now specifying multiple lines within one Graphics Primitive The vertex colors are only applied the first object. The workaround is easy by just defining individual Graphics Primitives, but i don't think this is the intended behavior.

Version 13.0

Version 13.1

dat = {Table[{Cos[x], Sin[x], x/10}, {x, 0., 10}], 
   Table[{Cos[x], Sin[x], x/10 + 2}, {x, 0., 10}]};
col = Map[RGBColor, dat, {2}];
pl = {
  Graphics3D[{PointSize[Large], 
    Point[Flatten[dat, 1], VertexColors -> Flatten@col], Line[dat]}],
  Graphics3D[{Thick, Line[dat, VertexColors -> col]}],
  Graphics3D[{CapForm["Square"], JoinForm["Miter"], 
    Tube[dat, VertexColors -> col]}, Lighting -> "Neutral"]
  }


dat = RandomReal[1, {150, 7, 3}];
col = Map[RGBColor, dat, {2}];
pl = {
  Graphics3D[{PointSize[Large], 
    Point[Flatten[dat, 1], VertexColors -> Flatten@col], Line[dat]}],
  Graphics3D[{Thick, Line[dat, VertexColors -> col]}],
  Graphics3D[{CapForm["Square"], JoinForm["Miter"], 
    Tube[dat, VertexColors -> col]}, Lighting -> "Neutral"]
  }
pl2 = {
  Graphics3D[{PointSize[Large], 
    Point[Flatten[dat, 1], VertexColors -> Flatten@col], Line[dat]}],
  Graphics3D[{Thick, 
    MapThread[Line[#1, VertexColors -> #2] &, {dat, col}]}],
  Graphics3D[{CapForm["Square"], JoinForm["Miter"], 
    MapThread[Tube[#1, VertexColors -> #2] &, {dat, col}]}, 
   Lighting -> "Neutral"]
  }