Public enough that people nearby died.

From the NPR:

BLUME: ...Mostly to the northeast of the state. However, fallout radiation was detected as far away as Rochester, N.Y., ultimately, so it did cover quite a bit of ground.

FADEL: Now, I can't get the image you open the story with out of my head - these campers, 13-year-old girls, playing in white flakes that are falling from the sky, thinking it's hot snow, not knowing it's hot ash from the nuclear blast. And then, only one of those girls made it to 30?

BLUME: Yeah. I mean, it's such a harrowing story, and, you know, again, totally flies in the face of the official narrative that nobody was in the area. They were only about 40 or 50 miles away at a summer dance camp, and it was 10 young girls around 13, 14 years old. They were jarred from their beds when the blast went off at 5:29 that morning. They were rushed outside by their dance instructor because nobody knew what had happened. They thought maybe a heater had exploded. And then, you know, a few minutes later, they see the flakes falling from the sky, and they think it's snow. But it's the desert in the summer in New Mexico.

FADEL: Yeah.

BLUME: But they were out playing in it. The apparent sole survivor of that episode described to me that they were so excited that they got into bathing suits and played in a nearby river and were pressing the snow into their faces, into their skin, and that it absorbed really quickly. And she said that - this survivor, Barbara Kent, who was 13 at the time - said that over the years, she began to hear disturbing reports that her fellow campers had fallen ill. And she says that by the time she reached 30, she was indeed the sole survivor.

Source: https://www.npr.org/2021/09/27/1040983335/survivors-of-the-trinity-nuclear-test-werent-warned-then-were-lied-to-after