It seems to me that, when playing Peonia, PTCGL puts the 3 selected cards on the first three unoccupied prize card slots. On the first match, you had slots (1,2,4,6) occupied prior to Peonia. Upon playing Peonia, you picked (1,2,4), leaving only the 6th slot occupied. Then, the first three unoccupied slots are (1,2,3), which are in fact where the Chanseys were placed. Had you chosen (1,4,6) rather than (1,2,4), this would've left the 2nd slot occupied. I suspect then that the Chanseys would have been placed on the (1,3,4) slots. Basically, the selected cards are not placed on the selected prize card slots, but rather on whichever first available slot there is. To be safe, always pick up the first three prize cards when playing Peonia.
in Miraidon's case the "rai" is actually part of "mirai" which means future (same as Koraidon's "korai" which means ancient, specially since Koraidon has nothing to do with thunders)
I built chansey with arc zard and used starbirth for clavell ( gets you 3 basics with 120 up or less) and peonia and took a single prize ko and chained 3 heads in a row to take a 4 prize turn ( I put them in slots 1,2,3 ) and then I took another and already had one prized and that flipped heads as well , luckiest game ever!