Electronic excitations are produced when matter is exposed to ion irradiation comprising highly energetic ions. These electronic stopping excitations are responsible for ion beam-induced DNA damage by energetic protons and a-particles, the chemistry and physics of which are central to burgeoning radiation cancer therapies. By simulating the non-perturbative electronic response of DNA to irradiating protons and alpha-particles, our first-principles dynamics simulations enable us to test the validity of the commonly used linear response theory description, and they also reveal unprecedented details of the quantum dynamics of electronic excitations. In this work, we discuss the extent to which the linear response theory is valid by comparing to the first-principles determination of electronic stopping power, the energy-transfer rate from ions to electronic excitation. The simulations show that electronic excitations induced by proton and a-particle irradiation cause ionization of DNA, resulting in the generation of holes. By studying the excited hole generation in terms of both the energetic and spatial details in DNA, our work reveals remarkable differences with the excitation behavior of DNA under more commonly used ionizing irradiation sources such as X/gamma-ray photons. Furthermore, we find that the generation of excited holes does not directly correlate with the energy-transfer rate as a function of the irradiating ion velocity, in contrast to what is often assumed in the chemistry and physics of radiation oncology.