Van der Waals heterostructures obtained by artificially stacking two-dimensional crystals represent the frontier of material engineering, demonstrating properties superior to those of the starting materials. Fine control of the interlayer twist angle has opened new possibilities for tailoring the optoelectronic properties of these heterostructures. Twisted bilayer graphene with a strong interlayer coupling is a prototype of twisted heterostructure inheriting the intriguing electronic properties of graphene. Understanding the effects of the twist angle on its out-of-equilibrium optical properties is crucial for devising optoelectronic applications. With this aim, we here combine excitation-resolved hot photoluminescence with femtosecond transient absorption microscopy. The hot charge carrier distribution induced by photo-excitation results in peaked absorption bleaching and photo-induced absorption bands, both with pronounced twist angle dependence. Theoretical simulations of the electronic band structure and of the joint density of states enable to assign these bands to the blocking of interband transitions at the van Hove singularities and to photo-activated intersubband transitions. The tens of picoseconds relaxation dynamics of the observed bands is attributed to the angle-dependence of electron and phonon heat capacities of twisted bilayer graphene.