We analyze the propagation of spatiotemporal Airy-Laguerre complex-variable-function Gaussian (ALCG) wave packets using phase modulation. These wave packets can split into left circularly polarized ALCG (LCP-ALCG) and right circularly polarized ALCG (RCP-ALCG) components due to circular birefringence in a chiral medium. Our discussion primarily focuses on the effects of polynomial order, angle parameters, distribution factor, cross-phase factor, first-order chirp factor, and chiral parameter on the ALCG wave packets. The distinct LCP-ALCG and RCP-ALCG wave packet characteristics are obtained, and the radiation forces on Rayleigh dielectric particles are investigated. Our results emphasize the influence of various parameters in the propagation properties of ALCG wave packets, unveiling their potential for advancements in optical communication and optical trapping domains.