In Sync

Take Melly's Metronographer++, from the box right in front of her.
Click the Temporal Investigator, behind and to the right of Melly.
Use the Metronographer on the Temporal Investigator.

I was hoping there was going to be an NPC named Tustin Jimberlake nearby but, alas, no. Bid the Temporal Investigator Bye Bye Bye and head north and slightly west.
Each subsequent Temporal Investigator is northwest of the previous one.

/way 53.36 84.63 Slowed down
/way 52.64 84.29 Sped up
/way 52.28 83.30 Reversed (entrance)

The slowed down Temporal Investigator is easy to see.
The Sped up one will be just that. He'll be running around a cabbage patch, quite a bit, so the coordinates are approximate.
The Reversed Temporal Investigator is inside a tower and the coordinates are to its entrance.

Quests in this series:

1 Time, Signature No prerequisite.
2 Pedgi the Parched
3 Downbeat Data
4 Compose Yourself
5a Grime Lies Where You're Killing Slimes
5b Slime Dies When You're Having Fun
6 In Sync <-- you are here
7 Feats Per Minute

Nice spongebob reference. If you see it you see it