Converting Black and White images to a specific rich-black for print with photoshop

We are preparing Black and White images for offset print.
The images will be printed on a black backgrounds and the printer suggested using this rich black mix in indesign: (50/40/30/100). 
I am now scared that the RGB images, that I will convert to CMYK (PSO Uncoted v3 Fogra52, as the printer suggested to export with) will turn out in a different black than the background set to the printes rich black (50/40/30/100)..
I converted my images in Photoshop to the printers colorprofile, but in the darkest areas, the image has a composition of about 88,60,45,89.
I suppose printing these images onto the black pages will result into a darker or ligher "frame" around my images due to the different composition.

I thought about making my own color profile but am unsure about some values.

Is there any way to tell an image its darkest value should be composed of something like 50,40,30,100?
Does it matter if the rich-blacks of the background are slightly different than the ones of my image?
50,40,30,100(background) vs 88,60,45,98(image) on quite open/rough paper (Munken print)?

Is there any save way to create a color profile for that, or is that advanced stuff.

Thanks for any hint ❤️