Yes....those $$ are reported as-if you received the $$, and then used them to purchase more.
You normally would-have received a 1099-DIV for those $$, and you just enter it in the software as-is. But if the total for your account, for everything from that broker was less than $10, they may not issue a 1099-DIV...but you are still responsible for reporting anything of 50cents or greater.
It will add to your basis in those shares though, when you eventually sell those shares.
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The only exception I know of, is if those stocks were held within an IRA or 401k, or the like...then those $$ would not be reported, because what happens within those retirement vehicles, stays there until you actually take money out.
Investors do have to report dividends as taxable income even if they reinvest them to buy more shares. Companies and brokerage companies will report such dividends on 1099-DIV forms the same way regardless of whether you reinvest in new shares, and the IRS will expect you to include them on your annual tax return. You should receive a 1099-DIV for the stocks that are in the dividend reinvestment program.
See the IRS FAQ about this.