This is not correct. The government sells treasury securities at auction.[1] Primary dealers are required to participate in all Treasury auctions.
When the Federal Reserve conducts open market operations, it does create reserves out of nothing, but most Treasury securities are not bought by the Fed. The Federal Reserve can buy treasuries directly from the government via non-competitive bids, but generally buys and sells treasuries on the secondary market via primary dealers.
> The government sells treasury securities at auction
This is true, in the sense that the Treasury and the Fed work together extremely closely, and both are acting as or on behalf of the government. But strictly speaking, it's the Fed that conducts the auction because it is the Treasury's fiscal agent.[1][2]
The link you supplied provides useful information for a retail investor who wants to buy securities, but it's not and it isn't meant to be a description of the fine mechanics of government funding. In the event that the TT&L accounts[3] and Treasury's account at the Fed are together insufficient for Treasury's spending needs, then it creates securities and transfers them to the Fed for auction, in exchange the Fed debits Treasury's deposit account. This all follows from the statutory limitations on both entities. Treasury isn't legally permitted to carry a negative balance at the Fed, but the Fed legally can carry a negative balance on its own account. A primary benefit of and reason for this arrangement is it makes the funding predictable. Personally I find the system elegant in its (legally mandated) complexity.
Saying "the Treasury sells securities at auction" isn't really wrong, seeing as it's just a simplification that is acceptable in virtually every case with the sole exception being discussions like this one. It's a lot like saying "I sold some AAPL stock." You didn't really, your broker did. In everyday conversation there's nothing wrong with these simplifications.
When the Federal Reserve conducts open market operations, it does create reserves out of nothing, but most Treasury securities are not bought by the Fed. The Federal Reserve can buy treasuries directly from the government via non-competitive bids, but generally buys and sells treasuries on the secondary market via primary dealers.
[1] https://www.treasurydirect.gov/indiv/products/prod_auctions_...