If there's any transparent object on the page and your Transparency Blend Space is set to CMYK or, if you have Overprint/Separation Preview turned on, the green will preview as it would convert to CMYK. For an all RGB preview set your blend space to RGB and turn off Overprint Preview.
Your image seems to be in an RGB space.
Your document settings are probably set up for CMYK output for print.
RGB and CYMK have different gamuts, that is the color spectrum which can be technically reproduced. In the greens and pink spectrum, the CMYK gamuts are much smaller than the RGB can do. So you will always get a different color if you try to print these lightning colors.
You can choose a different intent when converting the colors (to choose in the import options in the place image dialog) but differences will remain.
You have to live with it, either change your design or use a spot color which will increase costs.