With the most recent versions of iOS, when you import photos using iTunes import/sync or iCloud sync it will convert your transparent PNG file to a non-transparent JPG file. We reported the issue to Apple.
Until they resolve the bug use AirDrop, or download your PNG images from a weblink to get the transparent PNG file onto your device rather than sharing through iPhoto.
You can confirm that your file has been converted by pressing edit on the image on your device from the Apple Photos app (see below) If the background turns black then transparency has been maintained. If it stays white then the image has been converted to a JPG file.
If none of the above helps retrieve the transparency, consider using online software for background removal or reach out at firstname.lastname@example.org and we can help you with this.
Converted to JPG: