Since the Update 2 of Visual Studio, the TypeScript debugging in UWP apps is broken.
And here the solution (I assume you’re running in an English locale here, otherwise I don’t think the workaround is applicable):
In an administrator command prompt:
copy *.xaml en
copy TypeScript.Tasks.dll en\TypeScript.Tasks.resources.dll
The behavior that breaks the TypeScript integration in UWP (In reality, typescript is not officially supported in UWP apps, it will be in VS15 « next ») is potentially due to a TypeScript installation bug.