Milliseconds are probably recorded, but they are not used in group starts and it is not imperative to get more accurate times. The system has workeds well for decades and it exists as much to ensure fair racing as it is to ensure safety. Each rider gets the same time as the first rider in the group they are in. The group breaks and a new one is recorded when there is over one second gap between two consecutive riders. Thanks to this system the riders in the group do not have a need to rush to the finish line and cause dangerous situations, as they all know they will get the same time.
This article contains info about the technology: https://gearpatrol.com/watches/a267381/tour-de-france-timed . I suppose the spare bikes have transponders too and if a rider takes a spectator bike, as has happened a few times, they get the time from the finish line camera and adjust the results manually.
The UCI rules then state in section 2.6.015:
Where two or more riders make the same time in the general individual
time placings, the fractions of a second registered during individual
time trials (including the prologue) shall be added back into the
total time to decide the order.
If the result is still tied or if there are no individual time trial
stages the placings obtained in each stage, except team time trial
stages, shall be added and, as a last resort, the place obtained in
the last stage ridden shall be taken into consideration.
If anyone knows whether the last two clauses have ever been invoked, please let us know. It is vital cycling trivia to be used to impress the other pub patrons.
