SUMMARY
Since Wix# actually builds the MSI when you "run" the .exe it creates, and uses the WiX toolkit, you would need to output the executable Wix# + WiX Toolkit creates to your drop folder. Then make sure the WiX toolkit executable files are either on your PATH or in your output folder, and create Powershell script(s) that invoke your Wix# executable(s) in the drop folder. One straightforward approach would be to have one Wix# project for each separate "product installer", and have each these Wix# executables be output to your drop folder, for further processing/generation of the MSI files by your downstream Powershell (or other) scripts.
I am using Wix# integrated into the VS2013 IDE, so my answer should be interpreted in that context. My Wix# installer is simply one project of several in my overall solution.
EXAMPLE FOR A SINGLE Wix# PROJECT IN A VISUAL STUDIO SOLUTION
So, for example, if your Wix# project code file is set up in VS as a project named named MyWebsiteSetup, and the Wix# code file is MyWebsiteSetup.cs, your Wix# executable will be located at \MyWebsiteSetup\bin\debug\MyWebsiteSetup.exe.
Have the build place this MyWebSiteSetup.exe file in the drop folder, along with the other files Wix# places in bin\debug folder. Then have your second set of scripts run the MyWebsiteSetup.exe program, which will generate the MSI. I believe you may need to have the installation component files the Wix# code requires be deployed to the drop folder as well, and in the expected folder structure. Wix# seems to place all the other support files it needs in the bin\debug folder, so just having all the files copied from the Wix# project's bin\debug to the drop folder should get you what you need.
ADAPTING THE EXAMPLE TO MULTIPLE PRODUCTS (MULTIPLE Wix# PROJECTS)
Now, your question was how to do this for multiple websites where all the files are placed in the same drop folder. There are several ways to approach this, but the one I suggest is to have a separate Wix# project in Visual Studio for each separate product, and have the Wix# output files for each of those projects deployed to the drop folder along with the product files. If your separate products were named MyWebSiteSetupA, MyWebSiteSetupB, and MyWebSiteSetupC, they will generate executables MyWebSiteSetupA.exe, MyWebSiteSetupB.exe, and MyWebSiteSetupC.exe. You would simply have your second set of scripts invoke each of those in turn. Each of the Wix# code files (.cs files) for those projects of course will have been coded to know what files it needs to pick up when it runs, and when the resulting exe is run, it will get the files it needs, provided you've made them available where expected, and build the individual MSI's for each product's installer.
There are of course, numerous other approaches for this, with flexible tools like PowerShell, each approach with pros and cons, but I hope this helps get you started with an approach you can then tailor to your needs.