Why is SSMS showing red squigglies(sp?) even though the table exists?
In short, the tables are not recognized because the IntelliSense local cache is not up to date. 

While you are in the Query Editor window you can press CTRL + SHIFT + R to refresh the cache. This should update IntelliSense's cache and the red squiggles should disappear.

Please see this link for more information.