I believe the first 3 or so rare pulls in each treasure are guaranteed to be unique, after that, it's fully random.
And given that there are 8 rares(I think, others are super, ryt?), once you have 5, chances are you will get a duplicate.
Now, 3 duplicate in a row is on the unlikely side, but only barely, at 24% chance.

You are, as far as I know, the first one to complain about this on a treasure, but this topic have came up quite a few times on summon, which I'm sure you can imagine will encounter the repeating threshold much easier.

On a side note, using the coupon collector's problem, the estimated number of rares you need to pull before getting the full set is:
If 3 non-duplicate are guaranteed(including those first 3): 21.27
If 4 non-duplicate are guaranteed: 20.67
If 5 non-duplicate are guaranteed: 19.67

That is above par, as even with only 3 guaranteed non-dup the expected number of rare required is only 21.27, which means a bit under 1300 pull

But at the same time, 1500 isn't exactly far off from the par.

Assuming, that is, onoki is your last one, as the last one is the hardest (regardless of which it is), accounting for over 1/3 of the total required. If it's your second-to-last rare, then you are way above par, almost 2x.