Is there a physical substance there being warped? |

No.

Analogies can be dangerous. This analogy with a fabric can help you understand that space is warped by the presence of mass (Actually, it is more complicated then that, and things like momentum and pressure also contribute to the warping of space). But it can also give you the false impression that there must be some sort of physical substance that get warped. It mustn't. To better understand what meant by warping, think about the following questions.

Is the ratio between the circunference and the radius of a circle necessarily always equal to 2pi?

Is the sum of the three angles of a triangle always equal to 180 degrees?

Answer to both: Only if the space is flat!

For instance, we know that the surface of the Earth is not flat, even if we completely neglect mountains and other local features, because the Earth is a sphere.

Now make an equilateral triangle by starting ant the north pole, moving 10 000 kilometers southward all the way to the equator, then move another 10 000 kilometers eastward, and complete the triangle by moving 10 000 kilometers northward.

There you go, your triangle has three 90-degrees-angles for a total of 270 degrees!