There is no email triggered to those you've shared the file with if you modify it. You would have to let them know.
But more importantly, it depends on how you are editing the file as to whether or not a new file is created (which would not be shared).
For example, if you use the upload a PDF file, share it, and then use the Organize Pages feature, the rearranged file uses the same ID as the original one, and would keep its sharing relationships.
On the other hand, if you upload a Word document, then edit the original on your computer and upload the revised one, that will create a new file in Acrobat.com that would not be shared.
A quick test would be to see if the sharing icon is showing for the new/edited file:
Sorry for the slightly long-winded answer. Hope this helps.