Shrinkage induced cracking of thin material layers attached to a substrate gives rise to spectacular polygonal crack patterns. Examples range from drying lake beds through paint layers in art and industry to the columnar joints formed in cooling volcanic lava. In case of structural materials like concrete, restrained shrinkage results in undesired cracking which lets aggressive agents penetrate the material leading to an enhanced degradation. Laboratory tests on shrinking concrete have revealed that cracking proceeds in bursts which can be recorded in the form of acoustic noise. The b-value analysis of the acoustic event series proved to be an efficient tool to characterize the evolution of the shrinking system. To investigate shrinkage induced cracking phenomena, recently we have introduced a discrete element model which captures the essential mechanisms of crack nucleation and growth in the shrinking layer attached to a substrate, furthermore, the model allows for a representation of anisotropic material properties with a controllable degree of anisotropy. In the model the layer is discretized in terms of randomly shaped convex polygons, which are coupled by beam elements representing their cohesive contacts. Shrinking of the layer is modelled by gradually reducing the natural length of beams, while adhesion to the substrate is ensured by springs connecting the polygons to the underlying plane. Based on computer simulations of the model, here we investigate the temporal evolution of the accumulation of damage in the shrinking layer. In particular, we demonstrate that cracking of the shrinking layer proceeds in bursts which are cascades of correlated local breakings. Single cascades are characterized by their size, and duration, which both fluctuate in broad ranges due to the inherent disorder of the layer material. Our simulations revealed that the probability distribution of the burst size and duration exhibit power law behaviour with exponents which have a weak dependence on the degree of anisotropy. The size and duration of bursts are correlated since larger bursts typically grow for a longer time, which is expressed by a power law relation of the two quantities. Most notably, we show that the average temporal profile of cracking bursts has a nearly symmetric parabolic shape, which indicates that bursts start slowly then accelerate and stop gradually.