My understanding of the arrowhead device is that the unit the individual was with had to participate in the amphibious assault, glider, and parachute. A soldier or airman must be assigned or attached as a member of an organized force carrying out an assigned tactical mission. A soldier or airman must actually exit an aircraft or watercraft to receive assault credit. Individual assault credit is tied directly to the combat assault credit decision for the unit to which the soldier or airman is attached or assigned at the time of the assault. Should a unit be denied assault, no assault credit will accrue to the individual soldiers or airmen of that unit.
To answer your question on D+1,2,or 3 you would probably need to confirm rosters or Morning reports. Being in a unit that participated in an assault landing is basis for the award for an individual. But if individual was in the unit that participated but say "individual was in Hospital or Sick quarters" that individual probably would not receive the credit even though his or her unit received credit.
My understanding is that as long as the parent unit landed on a D-Day, then the soldier would qualify.
So taking our Texas units for example, if a soldier with the 133rd Field Artillery landed on D+1or D+2 at Salerno, he would still qualify for an arrowhead device because parts of his parent unit, the 36th Infantry Division landed on D-Day.
Texas Military Forces Museum
Dear Mr. Pritchett,
Thank you for posting your request on History Hub!
The United States Army Veteran Medals Home Page has a page on the Arrowhead device that provides some information. You may wish to contact the U.S. Army Human Resources Command Awards and Decorations Branch at email@example.com for specific questions about past and present award criteria.
We hope this is helpful. Best of luck with your research!