So soul society did want to eliminate both of them at one point.
Ginjo has a small amount of hollow in him like ichigo so i suspect him going all easy is just so it can be triggered. Dont think ginjo will go down that easy. Also it seem ginjo sword doesn't have any special powers? Cause it only fired a cero instead of a unique attack. What was his fulbring special ability again? So much could have been used, but wasnt. Think this is just the start of the whole battle