Modeling time means there is some way of e.g. evolving state over time, or projecting change over a period of time. Or being able to count time passing (without being told by external sources).

The LLM has no model of time. It is being called at regular times. If the cronjob misses two days or even a whole year of calling the LLM, the LLM will not respond any differently from if the cronjob was on time.