You will need to set up the workflow in a dynamic way. take a look at this tutorial to help get you started.

https://support.safe.com/hc/en-us/articles/25407480725645-Tutorial-Dynamic-Workflows

The feature reader makes it easy because it contains the “Schema” feature which comes out of the schema port. You can configure a write to look for the schema feature and use that to build the output table/attribute structure

FME does not know what to expect when the column-names change. Using the first row as attributenames could be helpfull but in your case it isn't.

So you should set up that FME reads the file without translating the columns to column-header-names. But keep the columnletter as the name.

Then in your workbench calculate what column index you want to read that day/week and rename those columns to what you want.

None of these worked. 

One thing that I want to highlight is that as long as I open the Reader settings manually, and hit “Ok” without touching anything, the Reader would appear to be refreshing something, and then the old script just works fine enough that it would include the new additional attributes. And then it works perfectly this way even after I restart my FME and run again (it would still fine all of the attributes), until next report comes in next month (means the path is changed and new attributes are added). So I think the logic is fine, I just don’t know how to implement this ‘touching’ or ‘refreshing’ behaviors of the FME so that it can kind of ‘touch’ the new file and automatically detect the new attributes. 

Eventually, I’m trying to automate this if my script runs with robustness. Thanks. 

What you want is not possible in FME.

That's why I suggested an alternate process, which is more complicated but possible.

Or you could try with autohotkey or something. So autohotkey could physically open your workbench, open the reader and open the properties. And then save your workbench.

Any suggestions from the vendor?