Different products using different indicators
An indicator does not affect a particular reaction. But in your solution, you have two successive reactions when adding HCl to this solution : First $$\ce{CO_3^{2-} + H^+ -&gt; HCO_3^-}$$ and a given indicator must be added to determine the end of this reaction. If you don't, all you see is a colorless solution being transformed into another colorless solution, even though its composition has changed. This added indicator may be phenolphthalein, which goes from red to colorless precisely at the end of this first titration. Then, by adding more HCl, you carry out the following reaction : $$\ce{HCO_3^- + H^+ -&gt; H_2O + CO_2}$$ And you need is another indicator, maybe methyl orange, to determine the end of this second reaction. The color of the methyl orange in solution changes from yellow to reddish exactly after the end of this second reaction.

Phenolphtalein and Methyl orange are molecules which reacts with $\ce{H^+}$ exactly like $\ce{CO_3^{2-}}$ and $\ce{HCO_3^-}$. But they react before or after these two ions. To summarize, $\ce{H^+}$ reacts first with  $\ce{CO_3^{2-}}$ and nothing else, and it takes a couple of milliliters to do it. Then it reacts with Phenolphtalein and nothing else, and it takes less than one drop to do it. Then it reacts with $\ce{HCO_3^-}$ and nothing else, and it also takes a couple of milliters to do it. And last but not least, it will react with methyl orange.