Dynamis - Killing a Time Extension with indirect weapon AoE does not grant Key Item

After killing the RearGuard Eye in Dyn-BCD and not getting the Time Extension/KI, I did some research into why it happened in Dyn-Tavnazia.

Platform: Windows 10
ISP: CenturyLink
Type of Internet Connection: Optical Fiber
Internet Connection Speed: 980Mbps
Date & Time: Sep. 10, 2021 5:45 MST
Frequency: Twice (Reproducible)
Character Name: Halon
Race: ElvaanM
World: Phoenix
Main Job: WHM, Lv.99
Support Job: THF
Area and Coordinates: Dynamis - Beucedine and Dynamis - Tavnazia
Party or Solo: Solo
NPC Name: None
Monster Name: Rearguard Eye and Statue Prototype
Steps:
At the Nightmare Makara in Dyn-TAV there's a Time Extension statue (Statue Prototype) where this test was performed.

Target a Makara and gain TP, then use an AoE WS such as Aeolian Edge (on Thf) in range of the Time Extension statue. Repeat this until the statue is dead - by targetting Makara and using AoE WS, never targetting the statue directly.

Notice that the Time Extension and Key Item are not granted when the statue dies.

The Time Extension and KI are correctly granted when the statue is targetted and an AoE WS is performed. They are not granted when the statue is not targetted and not killed directly.