The answer is that so far, that reaction has been fairly mild. Ten-year Treasury yields dropped by just 3 basis points the day the report came out, and stabilized the next day.
For the time being then, think of the rally for interest rates as being on hold. The rise in bond yields may pause, and the eventual response of savings accounts may be delayed, until clear evidence comes along to contradict the apparent slump in manufacturing. That may happen as soon as this Friday, with the May report on employment growth. However, if that report disappoints, expect bond yields to suffer a tumble -- and take with them the hope that savings account yields will rise in the near future.