1) make sure there is a bit of transparent bleed around the png graphic.
2) Import using the file explorer import, not copy and paste. That doesn't allow for the precise transparency as in Photoshop or other graphics program. I wouldn't use the "pick transparent color" function either, I just make my graphics ready in Photoshop or Illustrator and you should too.
When I use Illustrator I always copy and paste in Photoshop so I never export from the former. By exporting the PNG from Photoshop, I never had a problem.