I would be very careful about accusing a bartender of making your cocktail incorrectly unless you were physically sitting in front of them at the bar, you watched them make it the entire time, and the cocktail is one of the rare ones that can only be made a single way. Otherwise, you just come off like an asshole.
If you have specs you prefer for a cocktail that you made clear when ordering, and then those specs weren’t followed, then it’s OK to have the cocktail made again. Especially if the way it was made causes the drink to be drastically different in flavor or serve. For example, you asked for your Negroni to be served up instead of on the rocks, or you requested a specific gin for your Martini and they used a different one by mistake.
But if you didn’t watch the drink being made, you didn’t say how you wanted it made, and you still want to send it back because you claim it was made incorrectly, don’t be that person. Instead, simply tell the server you don’t like the cocktail and would either like to order a different one or have a glass of wine or beer instead.