The analysis of the spatiotemporal picture of particle radiation in relativistic heavy-ion collisions in terms of correlation femtoscopy scales, emission, and source functions allows one to probe the character of the evolution of the system created in the collision. Realistic models, such as the integrated hydrokinetic model (iHKM), used in the present work, are able to simulate the entire evolution process of strongly interacting matter produced in high-energy nuclear collisions. The mentioned model describes all the stages of the system’s evolution, including thermalisation and hydrodynamisation, which can help researchers figure out the specific details of the process and better understand the formation mechanisms of certain observables. In the current paper, we investigated the behaviour of the pion and kaon interferometry radii and their connection with emission functions in ultrarelativistic heavy-ion collisions at the Large Hadron Collider within iHKM. We focused on the study of the emission time scales at different energies for both particle species (pions and kaons) aiming to gain deeper insight into relation of these scales and the peculiarities of the mentioned system’s collective expansion and decay with the experimentally observed femtoscopy radii. One of our main interests was the problem of the total system’s lifetime estimation based on the femtoscopy analysis.