The best way to look at today is as a more sober attempt to hold the lowest yields in more than 3 weeks. The only day that's ended any better for bonds during that time is yesterday--an arguably more emotional example of forced buying stemming from a big, nasty sell-off in the stock market.
In contrast, stocks spend the entirety of today's trading session in better shape than yesterday afternoon. At times, they'd even recovered a majority of the ground lost over the past 24 hours. But even at those times, bonds weren't panicking.
Were bonds in weaker territory? Sure! But they weren't panicking. 10yr yields never went higher than 3.145 and they ended the session at 3.126. MBS had an even better day, finally turning the tables on Treasuries' recent outperformance (not uncommon to see that after a run of volatility gives way to a narrower trading day).
On the more pessimistic side of the coin, whereas bonds didn't panic, neither did they surge triumphantly toward stronger levels. We're forced to assume they'll need to see more stock losses before bigger bond gains become possible. There's no telling if economic data or earnings results will be more informative in that regard. The next big ticket item hits tomorrow morning with the first reading on Q3 GDP.