A tectonic cave is a secondary cave, but its formation has nothing to do with solution (corrosion) or erosion. The type of rock is nearly irrelevant to the forming of this cave type. The main force for the cave genesis is a tectonic force, mechanical stress moving rocks. Tectonic caves can be formed by any geological force that causes rocks to move apart.
The most common tectonic caves are Talus caves, which are formed by rock slides and collapses. Less common are Fissure caves which are also formed by rock slides, but in a different way. The Neotectonic caves are formed by glacial processes an are typical for Scandinavian countries.
And finally there is a related process happening inside caves, which is thus generally interpreted as an aging process of caves. It is called breakdown and is the collapse of rock inside caves. It does not create caves but may change existng caves substacially.