If you work in CMYK documents, you can change your color settings temporarily to sRGB when you want to export to png.
The problem is that Illustrator uses the RGB working space (in your example eciRGB) to convert your CMYK to a png file, but other applications assume (see as profile) sRGB and display the wrong colors.
Changing your RGB working space (temporarily) to sRGB wil correct this.
You could also solve the problem in Photoshop, but that is adding a couple of steps to get it right.
You can open the png file in Photoshop, Photoshop will see an sRGB profile. You can correct it by selecting Edit > Assign Profile and choose the eciRGB profile. After clicking OK you can select Edit > Convert to Profile and choose sRGB as destination space. That will make your file an sRGB document as most applications expect from a png file.