Based on the recent Famitsu translation, it looks like there is a lockout timer for loot for the entire week. I don't know whether it is character specific. However, I am HOPING that it is JOB SPECIFIC.
SE - Please make the lockout timer JOB SPECIFIC. If I queue up as a tank and get one item, I may not have an incentive to do the content for the remainder of the week. It would be more beneficial of my limited time to do treasure hunts, Extreme Primals or other content.
However, since the BIGGEST selling point of this game is playing MULTIPLE jobs on one character, I can queue up for the Duty Finder potentially every day. I have all jobs at 50 primarily because of 1.0 xp grinding. This is still very balanced because one item is going per JOB.
This works very well with the coil lockout mechanic because I can pick and choose which job to use for that week and have the necessary gear to tackle it on. By allowing me to enter the duty finder on a different job and still get rewarded, you will always have enough people joining to fill out the ranks for the entire week.
Otherwise, my other jobs fall further and further behind, and make it less enjoyable to play if I'm pigeonholed into selecting one job to gear up 3 months at a time.
This will promote variety and further strengthen the duty finder.
My 2 cents.