In an AVL system, an available unit is assigned based on its actual location.
In a non-AVL system, an available unit is assigned (and becomes unavailable) and replaces another unit, making that unit available. The unavailability of the relocator is concurrent with the availability of the relocatee, regardless of how long it takes to happen.
As an example:
If E258 was relocated to E265, with AVL, E258/265 could be picked for a call anywhere along the way from 258's quarters to 265's quarters.
Without AVL, E258 becomes E265-acting upon assignment. The CAD sees E265 as available and E258 as unavailable. E258/265 may pass occupied firehouses enroute to a call in E265's area, but would not be assigned a block from their own quarters even if they are just leaving.
This is where situational awareness by the Dispatchers is crucial. Situational awareness is not to be confused with discretion.
This is a general explanation of CAD systems. The specifics of FDNY are better explained by others.