14 CFR 105 covers parachute operations in the USA.
There is not a requirement for a NOTAM, but since this happened at an uncontrolled airport the nearest ATC facility must be notified at least 1 hour in advance but not more than 24 hours in advance and, they must have approval from airport management.
Then for the actual jump, ATC must be notified at least 5 minutes prior to jump via radio from the aircraft.
§105.23 Parachute operations over or onto airports.
No person may conduct a parachute operation, and no pilot in command
of an aircraft may allow a parachute operation to be conducted from
that aircraft, over or onto any airport unless—
(a) For airports with an operating control tower:
(1) Prior approval has been obtained from the management of the
airport to conduct parachute operations over or on that airport.
(2) Approval has been obtained from the control tower to conduct
parachute operations over or onto that airport.
(3) Two-way radio communications are maintained between the pilot of
the aircraft involved in the parachute operation and the control tower
of the airport over or onto which the parachute operation is being
(b) For airports without an operating control tower, prior approval
has been obtained from the management of the airport to conduct
parachute operations over or on that airport.
(c) A parachutist may drift over that airport with a fully deployed
and properly functioning parachute if the parachutist is at least
2,000 feet above that airport's traffic pattern, and avoids creating a
hazard to air traffic or to persons and property on the ground.
§105.25 Parachute operations in designated airspace.
(a) No person may conduct a parachute operation, and no pilot in
command of an aircraft may allow a parachute operation to be conducted
from that aircraft—
(1) Over or within a restricted area or prohibited area unless the
controlling agency of the area concerned has authorized that parachute
(2) Within or into a Class A, B, C, D airspace area without, or in
violation of the requirements of, an air traffic control authorization
issued under this section;
(3) Except as provided in paragraph (c) and (d) of this section,
within or into Class E or G airspace area unless the air traffic
control facility having jurisdiction over the airspace at the first
intended exit altitude is notified of the parachute operation no
earlier than 24 hours before or no later than 1 hour before the
parachute operation begins.
(b) Each request for a parachute operation authorization or
notification required under this section must be submitted to the air
traffic control facility having jurisdiction over the airspace at the
first intended exit altitude and must include the information
prescribed by §105.15(a) of this part.
(c) For the purposes of paragraph (a)(3) of this section, air traffic
control facilities may accept a written notification from an
organization that conducts parachute operations and lists the
scheduled series of parachute operations to be conducted over a stated
period of time not longer than 12 calendar months. The notification
must contain the information prescribed by §105.15(a) of this part,
identify the responsible persons associated with that parachute
operation, and be submitted at least 15 days, but not more than 30
days, before the parachute operation begins. The FAA may revoke the
acceptance of the notification for any failure of the organization
conducting the parachute operations to comply with its requirements.
(d) Paragraph (a)(3) of this section does not apply to a parachute
operation conducted by a member of an Armed Force within a restricted
area that extends upward from the surface when that area is under the
control of an Armed Force.
Even more information is available in AC 105-2E.