I believe Shilling has been predicting a deflationary environment. (Is that still the case?) In late 2008, when the fear of deflation ruled the market, TLT (long term treasuries) soared, while TIP tanked. This move has been reversed since then as deflation fears subsided. So they aren't always well correlated. I saw somebody quoting a 40% correlation index between TLT and TIP -- that seems surprisingly low to me.
In any case, if a fear of deflation returns, I would expect the same thing to happen -- TLT goes up, TIP goes down. But I guess it's up to you to decide if Shilling is correct about that. If I believed it, I would be selling all equities and buying TLT. But I'm not doing that. Time will tell if he's correct. Good luck.