The study of the fundamental properties of phonons is crucial to understand their role in applications in quantum information science, where the active use of phonons is currently highly debated. A genuine quantum phenomenon associated with the fluctuation properties of phonons is squeezing, which is achieved when the fluctuations of a certain variable drop below their respective vacuum values. We consider a semiconductor quantum dot (QD) in which the exciton is coupled to phonons. We review the fluctuation properties of the phonons, which are generated by optical manipulation of the QD, in the limiting case of ultra-short pulses. Then, we discuss the phonon properties for an excitation with finite pulses. Within a generating function formalism, we calculate the corresponding fluctuation properties of the phonons and show that phonon squeezing can be achieved by the optical manipulation of the QD exciton for certain conditions even for a single-pulse excitation where neither for short nor for long pulses squeezing occurs. To explain the occurrence of squeezing, we employ a Wigner function picture providing a detailed understanding of the induced quantum dynamics.