The origin of ultra-high-energy cosmic rays (UHECRs) is still an elusive question, mainly because the arrival directions do not point to a preferred source location. However, it has recently been
observed that the amplitude of the dipole anisotropy detected by the Pierre Auger Observatory increases with the energy. This can be interpreted as an indication of the presence of a dominant source in the direction of the dipole, depending on the effects of the Galactic Magnetic Field (GMF). However, alternative interpretations need to be rigorously examined and ruled out before any final conclusions on the dipole anisotropy can be accepted. Using CRPropa 3.2 and current GMF models, we find that UHECRs entering the Milky Way can experience delays of hundreds of kiloyears in the range of rigidities observed by Auger. Based on the constructed spectrum of ages for observed UHECRs, we explore the possibility that temporal changes in the flux of UHECRs can produce a dipole similar to that reported by Auger. We explore how discrete bursts can temporally modulate the UHECR flux and show that such injections can reproduce dipole-like anisotropies in idealized scenarios.