To me it doesn't seem like you are doing anything wrong on the changing strings side of things. I think you simply need to readjust your guitar!
Now be wary that string buzz can be caused by many things. And I would say that its impossible to completely eliminate string buzz as even custiom shop guitars have string buzz when played (I worked at a guitar store).
So to me, it comes down to 2 things:
- Your guitar needs to be readjusted. Sometimes, fret buzz is caused by the strings being too close to the fretboard. To resolve that, just need to readjust the truss rod and all of that.
- Adjusting your technique as well. Now I dont know you and your skills, so by no mean see this as an attack. Technique can be a huge factor. If your fingers are not positioned well or if the technique is not fluid, it will cause string buzz. And for this issue, patience and practice are your solution!
From the info you gave, this is what I think may happen. New strings have no impact on fret buzz by themselves. The only way changing strings can cause issue is if you drastically change the gauge of them but then again, this will affect the neck and the truss rod so it goes back to my first point!
Now I can invite you to also post a video of you presenting the issue and this will probably help us understand better your problem and will allow us to help you resolve this issue even more! All said and done, don't hesitate to ask if something wasn't clear or if you need more help!