Yes, they survived the blast. No, their survival was not unexplainable.
The Jesuits are at two locations: They reside at Novitiate of the Society of Jesus in Nagatsuke two kilometers from the edge of the city (and 3 kilometers from the epicenter of the blast), but at the time of the explosion some are at Central Mission and Parish House closer to ground zero.
While their survival was uncommon, it was not exceptional. Thirteen percent of the 31,200 people living within one kilometer of ground zero survived the blast, according to this map on Hiroshima and Nagasaki Remembered, (Computed from data in A. W. Oughterson and S. Warren (Editors), "Medical Effects of the Atomic Bomb in Japan," McGraw-Hill Book Co., Inc., Chapter 4, 1956). From 1.0 to 2.5 kilometers, 73% survive; from 2.5 to 5 kilometers, 98% survive.
According to The Avalon Project at Yale Law School:
The central portions of the cities underneath the explosions suffered
almost complete destruction. The only surviving objects were the
frames of a small number of strong reinforced concrete buildings which
were not collapsed by the blast; most of these buildings suffered
extensive damage from interior fires, had their windows, doors, and
partitions knocked out, and all other fixtures which were not integral
parts of the reinforced concrete frames burned or blown away; the
casualties in such buildings near the center of explosion were almost
The Novitiate was on a hill above the city of Hiroshima, according to Siemes. The parish house was in the city next to the church school. Both Siemes and Father Wilhelm Kleinsorge say the wooden structures built by "Brother Gropper" were heavily reinforced due to Gropper's concerns about earthquakes.
Kleinsorge later related his experiences to reporter John Hersey, whose Hiroshima was published in The New Yorker:
Father Kleinsorge never knew how he got out of the house. The next
things he was conscious of were that he was wandering around in the
mission’s vegetable garden in his underwear, bleeding slightly from
small cuts along his left flank; that all the buildings round about
had fallen down except the Jesuits’ mission house, which had long
before been braced and double-braced by a priest named Gropper, who
was terrified of earthquakes
Siemes wrote a separate account of his experience starting at the Novitiate, which he later determined was 3 kilometers from ground zero:
I jump to the window to find out the cause of this remarkable
phenomenon, but I see nothing more than that brilliant yellow light.
As I make for the door, it doesn't occur to me that the light might
have something to do with enemy planes. On the way from the window, I
hear a moderately loud explosion which seems to come from a distance
and, at the same time, the windows are broken in with a loud crash.
There has been an interval of perhaps ten seconds since the flash of
light. I am sprayed by fragments of glass. The entire window frame has
been forced into the room. I realize now that a bomb has burst and I
am under the impression that it exploded directly over our house or in
the immediate vicinity.
Down in the valley, perhaps one kilometer toward the city from us,
several peasant homes are on fire and the woods on the opposite side
of the valley are aflame. A few of us go over to help control the
flames. While we are attempting to put things in order, a storm comes
up and it begins to rain. Over the city, clouds of smoke are rising
and I hear a few slight explosions. I come to the conclusion that an
incendiary bomb with an especially strong explosive action has gone
off down in the valley.
The survivors from the parish house later told Siemes about their experience: "The Church, school, and all buildings in the immediate vicinity collapsed at once." Valuables were removed from the rubble and buried in a clearing to protect them from the spreading fires. "Father Schiffer was buried beneath a portion of a wall and suffered a severe head injury. The Father Superior received most of the splinters in his back and lower extremity from which he bled copiously."
Kleinsorge and another priest soon display symptoms of what may be radiation exposure, Siemes wrote:
Father Kleinsorge and Father Cieslik, who were near the center of the
explosion, but who did not suffer burns became quite weak some
fourteen days after the explosion. Up to this time small incised
wounds had healed normally, but thereafter the wounds which were still
unhealed became worse and are to date (in September) still
Siemes was doubtful of radiation's effects and suspected the poor healing was due to malnutrition.
Kleinsorge suffered terribly. Hersey relates the story of what happened to the priest, dating it to about three weeks after the explosion as he was walking back from an errand:
His knees grew weak. He felt excruciatingly tired. With a
considerable expenditure of spirit, he managed to reach the Novitiate.
He did not think his weakness was worth mentioning to the other
Jesuits. But a couple of days later, while attempting to say Mass, he
had an onset of faintness and even after three attempts was unable to
go through with the service, and the next morning the rector, who had
examined Father Kleinsorge’s apparently negligible but unhealed cuts
daily, asked in surprise, “What have you done to your wounds?” They
had suddenly opened wider and were swollen and inflamed.
These four [Kleinsorge and three other survivors] did not realize it, but they were coming down with the
strange, capricious disease which came later to be known as radiation
Kleinsorge would be hospitalized in Tokyo for four months and was back in the hospital a year later.
According to this 1984 New York Times review of Hiroshima:
Suffering from fever, diarrhea and utter exhaustion, [Kleinsorge's] was a classic
case history of ''A-bomb sickness.'' But he bore this life of misery
''with the most extraordinarily selfless spirit,'' continuing the
self-abnegating pastoral life. In 1961, his energy flagged, and he
developed liver dysfunction, high blood pressure, back and chest
pains. On his hospital chart in 1976 was written ''a living corpse.''
He died the next year.
As of 2007, there were 226,598 officially certified survivors of the atomic bombings still alive in Japan, according to Children of the Atomic Bomb.
One note: many of the stories about the Jesuits use this image:
Which is the concrete remains of the Nagarekawa Methodist Church of Christ, a Protestant church, not a Catholic Church or Jesuit mission. The actual mission is located behind it, visible in this link: https://bigpulpit.com/2018/12/17/monday-afternoon-edition-76/