peer review - Should referees assume that authors will see the full report if their paper is rejected?

I have now more than once had the following series of experiences as a referee of mathematics papers:

1. 
   
   

   Elite Journal A sends me a paper. I find some problems with it, some small and some large, and describe them in a carefully- and thoughtfully-written report, but also tell the editor that even if the problems were fixed I do not think that the results are sufficiently interesting to rise to the august standards of EJA, though the results would deserve publication somewhere.

   
   


2. 
   

   Several months later, Mediocre Journal B sends me the same paper. The author has clearly not incorporated anything from my earlier report: typos that I pointed out have not been fixed even though it would have been trivial to do so, and the more serious problems that I found have not been addressed at all.

   
   

The first time that this happened I was quite upset with the author: based on my earlier report he had been made aware of fundamental flaws in the proof of his main result, yet he had the nerve to try to publish it anyway. But since it has happened again (with a different author), it has occurred to me that maybe what is happening here is that the author simply is not getting a chance to see the report, because the editor isn't sending it with the rejection email.

Is there a consistent practice in this regard? When I have had papers rejected I suppose I often haven't gotten a detailed report with line-by-line corrections, but I usually assumed that one had not been written (most of my rejections have happened fairly quickly and on grounds of significance as opposed to correctness). If I want the author to see my report even if the paper is rejected, do I need to specifically tell the editor this? Or have I just happened to stumble across some unscrupulous authors?