With vinyl, you need to make sure you don't have overlapping paths. That's probably what you printer is referring to.
Maybe the issue the printer has is because you didn't clean up your graphic by using the "pathfinder" tool and having transparent filling and/or white instead of transparent.
Your strokes should also be "expanded."
Mini guide here.
If you did this in InDesign, first thing to do is to export all this in PDF. Then you'll be able to open and modify your montage in Illustrator.
I made an example with 2 smiley faces overlapping.
If you look in the menu "view/preview", you will notice the lines overlapping. It's not ideal for vinyl cutting even though when you look at your artwork in normal view it looks normal. What you want is to remove the overlapping parts.
First, expand all strokes. Vinyl cutting cannot really read the thickness of strokes. They only need the outlines.
Select all > Then go in the menu "Object" and select "Expand"
Check the 2 boxes in the window "Expand"
Then what you need to do is to cut everything in order to remove the extra parts you don't need... If you use the "Divide" in parthfinder, it will separate the overlapping parts from the rest and will be easy to remove.
Select all, then on the Pathfinder tool, select "divide"
Now you need to remove the white parts. Unless you need to print in white and black, the white parts are usually representing transparency. Do this step if your vinyl is black only.
Use the Direct Selection Tool (white arrow) and click on a white part of your artwork to select it. Then go in the menu "Select" and choose "select same fill and stroke". Then delete that white.
Now all your have left is your black with the outline but also some paths that could be merged to simplify your vector.
To merge all your black together, click on one portion of your black and then go again in the menu "select" then choose "select same fill and stroke"
Then go on the Pathfinder tool, and click "merge". It will assemble together all the black parts of your artwork.
Finally, you want to remove all the transparent paths and shapes left.
Take the rectangle tool and trace a box with no filling and no strokes.
Then select this box, go in the menu "select" and choose "select same fill and color". Press delete!
If you select all in your artwork, you will know if you did a good job because all you'll see is black in the color swatch. That means no white or empty paths are left, and no strokes either.
And the outline view should look like this, where nothing is overlapping anymore.