Helpful if you would give the city pairs and flight(s) numbers - here is the BIG WORD "Timely".
After 24 hours can't see anything as Delta archives the passenger record flight history.
It used to be that a person with supervisory credentials could look into the history; but
this is not going to happen unless a very serious breach of non-rev conduct happens.

After the fact ???s - were there enough seats for the entire family to get on a flight ?
If not then the family more in likely let junior seniority/pass order take the vacant seats so
the family could travel together.
Now the flight that shows them with seat assignments it would be presumed that they are
onboard "IF" their boarding passes where scanned - also a possibility that the family was
boarded at the last minute rushed onboard skipping the scanning process.
Last ? did the family have more listings for today or other flights ?
Often times a non-rev will list for more than one flight so that the need to make another
listing when remotely away from access to the DeltaNet - TravelNet can be skipped.
Courtesy note - Please cancel all unused listings !
If not the Non-Rev Standby List is skewered with misleading information.
The Airport Standby List is not - this list shows persons rev and non-rev awaiting a seat