It is legal for a property owner to have a vehicle towed off of their property, if the vehicle is there without permission. If you have a vehicle with expired tags, your permission to park there may have been rescinded as of that notice. It is possible that a parking spot is part of the lease, in which case it would be a breach of contract for them to have your car towed. However, even if it's in the lease, if it is required by law, or specifically mentioned in the lease (i.e. "must be registered"), it is legal to tow the car.
The city claims the right to regulate vehicles even parked on private property:
Abandoned vehicles are defined as: vehicles that do not bear a license
plate, or on which the displayed license plate is invalid, unless said
vehicle is stored within a completely enclosed building or unless it
is stored on a bona fide sales lot or an automobile storage yard or
automobile wrecking yard, which threaten or endanger public safety or
welfare; create a blighting influence upon the neighborhood where the
vehicle rests, or; is, or may reasonably become, infested, or
inhabited by rodents, vermin or other animals, or may furnish a
breeding place for rodents, vermin or other animals. Inoperable, when
referring to a vehicle, means the vehicle is incapable of being
immediately driven, moved, or pulled in the manner for which it is
intended or designed.
The specific underlying ordinance Sec. 518.203(1) says
No person in charge or control of any property within the city whether
as owner, tenant, occupant, lessee or otherwise, shall allow any junk
or abandoned vehicle to remain on any private or public property
within the city longer than 15 days; and no person shall leave any
such vehicle on any property within the city for a longer time than 15
days; except that this article shall not apply to a vehicle on the
premises of a business enterprise licensed and operated in a lawful
place and manner, to repair vehicles with current license or those
places where active restoration is taking place and both activities
are taking place within a closed building.
An abandoned vehicle is defined as
a vehicle that does not bear a license plate, or if the displayed
license plate is invalid, unless said vehicle is stored within a
completely enclosed building or unless it is stored on a bona fide
automobile sales lot or an automobile storage yard or automobile
The ordinance does not apparently define "valid license plate", but from state law, we can determine that you affix a "validation sticker" to your "registration license plate", so without a current tag, the license is not valid.
Apparently the practice of towing cars with expired tags is not isolated in Florida: an untagged vehicle may not be visible to the public.