Not all formats support transparency
PNG can contain transparency and WebP can too. JPG does not have an alpha channel, so transparent areas need to be converted to a background color.
If you need transparency, do not export to JPG
Choose PNG or an alpha-compatible format. Then review the result against a checkered pattern or different background colors to check the edges.
Why does a white background appear?
When you export to JPG, an application may fill transparent areas with white. It's not a viewer error: the final format simply needs real color in those pixels.
Take care of halos around the object
If an image was originally designed on a colored background, the semi-transparent borders may retain some of that tone. Specially review logos and cutouts before publishing them on another background.
Save a master copy
For graphical elements that you will reuse, keep a good quality PNG transparent version. From it you can produce copies JPG with different backgrounds whenever you need them.
Do it directly in Luna4
Process your image in the browser and review the result before downloading.
Convert while preserving transparency