"tumble back" is correct and usable in written English.
You can use it to describe a person moving or being moved quickly and/or unexpectedly, such as, "The startled cat tumbled back down the stairs."
Ben Bernanke warned that America could tumble back into recession unless there is a deal on the fiscal cliff soon.
"I did not tumble back in a white beam of enlightened reverie, scales falling, realising that the Westminster machine, with a different pilot will serve ordinary people.
That is, before our fear ebbs and we tumble back into indifference, as we have about swine flu, SARS and even AIDS.
It's the prospect that our economy, climbing weakly out of a severe recession, might tumble back into the financial slough of despond.
As 2013 approaches, neither team looks to be in particularly good shape, raising the question of whether this season could again see them tumble back under.500 together.
When Sisyphus neared the summit, the boulder would slip from his grasp and tumble back down to the bottom of the slope, forcing him to start again.
