The timeline is this:

In 1947, the Soviets announced that there was no secret to the atomic bomb. Molotov put it as such:

As we know, a sort of new religion has become widespread among expansionist circles in the U.S.A.: having no faith in their own internal forces, they put their faith in the secret of the atomic bomb, although this secret has long ceased to be a secret.

This was dismissed as posturing; the US analysts just rejected it as him saying what many scientists had said (there was no essential secret to making nuclear weapons), not as evidence of them possessing a weapon. (Which was the correct interpretation, but bear with me).

In August 1949, the Soviets tested their first bomb. They did not announce the test and from what we can tell had no intention of announcing it. There were many reasons for not announcing it, including: 1) they didn't actually yet have a deployable nuclear capacity (they only had one bomb, and they tested it — it would take time to build up a real arsenal, and letting your enemy know that you're on the nuclear threshold is a dangerous thing to do), 2) the Soviets don't announce things like that during this time period; secrecy was the default position, and 3) you can always announce later if you feel it's useful — once you say something, you lose that flexibility.

The US had been monitoring for radiation from a test and in September 1949 detected it. They figured out it must have been a bomb. They noted the Soviets had not announced it. They debated whether they ought to announce it. Truman was initially afraid it would tank the British economy (it was struggling) if he announced it, but his advisors convinced him it would be infinitely better if the US announced it (and explained that they were still in control, etc.) than to have the Soviets announce it. They feared the Soviets might announce it at the next big party meeting (though it isn't clear that would have happened, but it's a totally plausible thing for the Soviets to do in the abstract). Truman then announced it (though even then, he carefully did not indicate it was a bomb, but an explosion — but everyone correctly interpreted it as an explosion).

In response to Truman's announcement, there was a huge flurry of international attention and activity. It was a major issue and story! The Soviet government was a little taken aback by the announcement themselves. Anyway, they felt the need to address the Truman announcement, and so TASS released the following statement:

As for the production of atomic energy, TASS deems it necessary to recall the fact that already on November 6, 1947, the Minister of Foreign Affairs of the U.S.S.R., V. M. Molotov, made a statement concerning the secret of the atomic bomb, saying that “this secret ceased to exist long ago.”

This statement signified that the Soviet Union had already discovered the secret of the atomic weapons and had this weapon at its disposal.

Scientific circles of the United States of America regarded this statement by V. M. Molotov as a bluff, considering that the Russians would not be able to master the atomic weapon earlier than the year 1952. They were mistaken, however, since the Soviet Union has found out the secret of the atomic weapon as early as 1947.

As for the alarm that is being spread in this connection by certain foreign circles, there are not the slightest grounds for alarm. It should be pointed out that, although the Soviet Government has the atomic weapon at its disposal, it adheres and intends to adhere hereafter to its old position in favor of the unconditional prohibition of the use of the atomic weapon. Concerning control over the atomic weapon, it has to be said that this control will be essential in order to check up on the fulfillment of the decision on the prohibition of the atomic weapon.

So, anyway, their "confirmation" was them saying, "guys, we told you ages ago we had the bomb, but you laughed at us, so whatever. This is not news." (Which was, of course, a bluff of sorts.) It was a reaction the announcement by the US; they were not, apparently, intending on announcing it at that time.

The complications behind the test, the announcement, and the aftermath are covered in depth in Michael Gordin's Red Cloud at Dawn, which is also just a good read in general!