This is kind of a big question, but I will try to give a basic explanation:
InDesign has some settings called Edit > Color Settings... where, among other things, Working CMYK is defined. Every new document will get these settings by default.
Your document also has a setting called Document CMYK which can override Working CMYK.
This is the CMYK profile chosen (consciously or not) for converting RGB (and other non-CMYK) images and colors to CMYK.
When turning on View > Overprint Preview your document is shown as it would look if it was converted to Document CMYK. Very bright RGB colors lie outside what is possible to print with CMYK, so they will get noticeably desaturated.
But you haven't turned on Overprint preview so why are you seeing this? That is because when placing anything with some kind of transparency (using a blend mode, effect or having lower opacity than 100%) on a spread will force Overprint Preview to be turned on! Otherwise InDesign can't draw the artwork.
There is no way to "fix" this, since it is not an error.
If you are making a document which will only be shown on a screen, you can avoid this problem by creating a Web document to begin with. This will have Edit > Transparency Blend Space set to Document RGB instead of Document CMYK.
But if you are making a document for print, you will have to accept that there are colors which can't be reproduced on paper. To get the best possible conversion you need to find out which CMYK profile to use for the specific printing device and paper type you have in mind (ask the print shop). And when you are exporting your final pdf, you need to convert all RGB to this profile.