What must I do when I receive postgres on conflict documentation?

 I am attempting to run a Postgres UPSERT in fairly concurrent code. I have been seeing a duplicate key value that violates a unique constraint error when my service is under load.

By way of a reduced example, I have the following table, which has an id primary key and an id_secondary unique key (meant to function as a second ID)

CREATE TABLE "test_table" (
    "id" text NOT NULL,
    "id_secondary" text NOT NULL,
    "value" bool NOT NULL DEFAULT 'FALSE',
    PRIMARY KEY ("id")
);
CREATE UNIQUE INDEX "test_table_uc" ON "public"."test_table" USING BTREE ("id_secondary");
I am running the following two statements simultaneously:
INSERT INTO "test_table" ("id", "id_secondary", "value") VALUES('1', '1', 'false') 
ON CONFLICT ("id")
  DO UPDATE
  SET "value" = "excluded"."value";
INSERT INTO "test_table" ("id", "id_secondary", "value") VALUES('1', '1', 'true') 
ON CONFLICT ("id")
  DO UPDATE
  SET "value" = "excluded"."value";
and it is my expectation that whichever statement executes last will be the one to set the value of "value".
Occasionally I am receiving the error duplicate key value violates unique constraint "test_table_uc" from one of these statements. My full test setup in Go (using testify) is:
suite.Run("Concurrency", func() {
    db, err := sql.Open("postgres", "host=localhost port=35432 dbname=test sslmode=disable user=postgres")
    db.SetMaxOpenConns(10)
    suite.Require().NoError(err)
    for ii := 0; ii < 100>        wg := sync.WaitGroup{}
        wg.Add(2)
        go func() {
            _, err := db.Exec(`
                    INSERT INTO "test_table" ("id", "id_secondary", "value") VALUES($1, $2, 'false') 
                    ON CONFLICT ("id")
                        DO UPDATE
                            SET
                                "value" = "excluded"."value"
                `, ii, ii)
            suite.Require().NoError(err)
            wg.Done()
        }()
        go func() {
            _, err := db.Exec(`
                    INSERT INTO "test_table" ("id", "id_secondary", "value") VALUES($1, $2, 'true') 
                    ON CONFLICT ("id") 
                        DO UPDATE
                            SET
                                "value" = "excluded"."value"
                `, ii, ii)
            suite.Require().NoError(err)
            wg.Done()
        }()
        wg.Wait()
    }
})

Where I am allowing concurrent SQL connections using db.SetMaxOpenConns(10) and the go func() syntax is running both SQL statements in different goroutines (threads). Only two of the statements are run at a time, and the value of "id" and "id_secondary" are always set to the loop iteration. I wait for both statements to return before iterating.

It generally fails if the duplicate key value violates a unique constraint error within a few loops.

I have not modified my isolation settings and I am running in SHOW default_transaction_isolation = read committed, on PostgreSQL 9.6.24

My Question

At no point is the statement generating a row that does not satisfy the unique constraints of the table. Seemingly, both statements are attempting to insert data at the same time. The Postgres documentation states that:

ON CONFLICT DO UPDATE guarantees an atomic INSERT or UPDATE outcome; provided there is no independent error, one of those two outcomes is guaranteed, even under high concurrency. This is also known as UPSERT — “UPDATE or INSERT”. which I interpret to mean that the INSERT or UPDATE happens atomically, they should never attempt to write in data with the same primary key.

For the test_table_uc constraint to be violated, then in my example, the primary key uniqueness constraint must also be breaking. This is very surprising to me.

What am I missing here?