With just two words, “Well actually”, you sound like a condescending over-explainer. You come across as rude, pretentious, and self-centered.
In those words, your listener hears: “I’m right and you’re wrong.” And they will think to themselves: “You think you’re superior and that I’m stupid.” That may not be your intention, but that it generally how it comes across.
If you find yourself saying “Well actually” often, reflect about where it is coming from: Are you needing to sound smart? Did you grow up in a competitive family and you wanted to prove you were smarter than your siblings? Are you trying to show people that you’re the person with the most interesting take on the issue? Maybe it comes from a need to shine, to have the spotlight on you.
As you feel those words about to slip off your tongue, think: Is a correction necessary? Even at the expense of your relationship? You may be better off reminding yourself that even though you know things, that doesn’t mean everyone else needs to.
If you feel that it is important to share the correction, do it with grace and respect. You might start the sentence with, “From what I understand” or “From the information I have”. That allows for the other person to add to what you say, or even agree with you.