Have you declared virtual applications in the App Service?
What method are you using for publishing?
When you open the App Service and browse the files, has the publish "cleaned" the other apps files up?
My gut is that you're using a simple deployment mechanism like ZipDeploy via Visual Studio Publish Profile that is not correctly deploying for your configuration when you're deploying over the top.
Deploying two projects to one App Service isn't a problem, but requires testing and optimising your deploy.
I think what you'll need to do is; better prepare your files locally, before then doing a single deploy command. My preference on deploying to App Service is with GIT source binding rather than a Visual Studio Publish.