A colour expressed as cmyk 100/11/3/16 isn't a standardised colour, its a recipe for mixing ink. It may look radically different according to the printer/ink/paper. This is why Pantone have abandoned CMYK in their cards, moving to Lab.
For you to try to match it you need to set a suitable CMYK working space, and make sure you have suitable conversion to the correct device space when you print. Otherwise it's just random numbers.
You shoulld NEVER use EPS nowadays in InDesign.
If the file comes from Illustrator save as AI and place that.
But Illustrator is not a common PDF editor.
You should NEVER open a PDF which comes from the client, unless it was created in Illustrator and with the Illustrator editing capabilities.
You can place a PDF in InDesign.
If the PDF from the client does not meet the printing requirements, ask for a new one.
The color conversion from spot colors should be done based upon Lab values, they might not match any tables you have got.
>>> Your described workflow is not very trustworthy.
I am currently working in illustrator and am quite a amateur!!
Ok so Here is the process I follow to try ensure the flatbed digital printer prints my colours correctly.
1 -Open up artwork(PDF) from client
2 -Save a copy(AI) to create master file [Ive found that in this process of saving an Ai file, unchecking the "Use compression" tickbox has dramatically improved my colour but it is still not perfect]
3 I open the PDF I have just saved, in Photoshop to create an EPS with the actions function, for my print department
4 [I know you can create an EPS directly from illustrator but to have the correct crop/tig marks and blleds, this is simply the easiest way]
5 -They then open our EPS and do their set up.
6 Our colour output from the printer is not correct and we cant seem to match it to what we require .
1 - Opening a PDF in Illustrator is completely wrong.
Illustrator is not a PDF editing program.
2 - I'm lost for words
3 - Opening a PDF in Photoshop completely flattens the entire file, rasterising every single piece of vector artwork - it's a completely mad workflow and no need for it at all.
4 - Photoshop EPS and Illustrator EPS are not the same thing at all.
5 - I'd love to know what hack they are doing once you send through your hacked files
6 - I'm not surprised
The easiest workflow is to get the original files it was created in and use that program to make the edits and final files.
You can open up the supplied PDF in Acrobat and check the File>Properties and it should indicate what Program created the file.
Ask the person who supplied you the file to supply the artwork file.
Open the files in the correct program and work from there.
Stop opening PDFs in Illustrator
Stop saving as EPS files
Stop opening PDFs in Photoshop
Why can't your department deal with print ready PDFs?