The incident came a week after a woman was reportedly blinded in one eye at the Ryder Cup after being struck by a tee shot hit by world No.3 Koepka.
Hatton spoke to her when she returned to her feet and she was later seen walking to a golf cart and smiling as she was taken to an on-site medical centre.
A female spectator was struck in the head by the foul ball and was shown bleeding from the wound.
The course is one of the three used for the pro-am event.
"Yesterday was probably one of the worst days of my life", Koepka said in his pre-tournament press conference on Wednesday.
Hatton's Ryder Cup team-mate Tommy Fleetwood recovered from a poor start to play his last eight holes at Kingsbarns in four under par to record an opening 71.
It was sharp improvement for Fraser who has yet to record a top ten in 2018 and is now in 175th position in the Race to Dubai ranking.
"But I can't let it affect me on the golf course".
The pair lead by one but looming just two behind are Ryder cuppers Brooks Koepka and Tyrell Hatton, Koepka able to out behind him the drama of last week and its aftermath with a round of 70 at Kingsbarns.
'"I was getting updates when I was out on the golf course, because I wanted to know how she was doing, and when I finished my first nine holes, I got told she was OK".
All 168 players in the field will play a round on each course, before the final round takes place at St. Andrews on Sunday.
Hatton's round, too, was at Kingsbarns and the victor of the event in each of the last two years is lurking as a real chance to three-peat.