This isn't about the time display, but rather the sun icon that moves around the mini-map corresponding to the hours of the clock. During the p.m., it moves normally; but during the a.m., it just sits at each hour for three minutes and then jumps directly to the next hour.

(As a gatherer, this can be frustrating when the map shows I'm just in time, but as soon as I spend all my GP the node suddenly disappears because it was actually 2:47 and not 2:00... >.> )

I've mentioned this to a few groups in game to see if it's just me, but most people have ignored me. When I do get a response, it's usually limited to "Oh, I don't even look at that." Although, one person did take the time to explain that clicking on the time display will change it between local, server, and Eorzea time. It didn't really address the issue, but thanks, Captain Obvious. </thumpsup>

I did check multiple characters on multiple servers (in both NA and JPN data groups) on both PS4 and PC.

Time: Consistently 12am-12pm Eorzea time, every day. (12:20-12:56am server time, and alternating 36min periods before and after.)
Frequency: Every day, Eorzea time
World name: Multiple - Ultros, Durandal
Character name: Multiple - Isen Gard, Maiandra Hyatt, Mercury Lampe, others
Retainer name: n/a
NPC name: n/a
Monster name: n/a
Class/Level: Multiple - MIN60, BTN60, SMN60, MCH40, ARC12, etc
Party or solo: Solo
In-game time: 12am-12pm, every day
Area and coordinates: Everywhere - Idyllshire, Mist, Limsa Lower, Old Gridania, Azys Lha, Hinterlands, etc

Housing:
Steps:
1. No steps. Time moves on its own, independent of my actions.

Connection Specs
- Type of internet connection/provider Verizon Fi-OS
- Modem maker/model number Actiontec MI424WR

Model Number of the PlayStation®3 You Are Using
- Model Number: n/a

Model Number of the PlayStation®4 You Are Using
- Model Number: CUH-1001A

Model Number of the PlayStation®Vita You Are Using
- Model Number: n/a

Information About the Peripherals You Are Using
-Type: USB headset
-Maker: Turtle Beach
-Model Number: TBS-3308-01

-Type: USB keyboard
-Maker: Dynex
-Model Number: DX-MKB101

-Type: "Dualshock 4" Controller
-Maker: Sony
-Model Number: BLUE?