Ableton explains in there Knowledge Base that latency and jitter are a problem of most computers, because the internal timings for audio processes are not of a high enough priority. They have made the decision that latency is acceptable but jitter not. They say, Ableton Live checks during the recordind the time-stamps of all samples coming from the audio interface (here the AR/OB) and buffers and get’s them all in place correctly. This process prevents jitter, which would destroy any kind of groove, but cannot prevent latency too.
AFAIK the only workaround is, to free as much CPU for the recording (there are some CPU hungry culprits like “reverb” or some high quality soft-synths … to name one, Diva by u-he), to make buffer sizes as small as possible, and to check on each clip and do the required work manually to get the transients in place. If the clip is tight “inside” and only shifted little to others, then only a correction of the start/beginning of the clip is required to get clips tight to the clock.
It’s not guaranteed that internal latency correction measures of Ableton Live get this sorted out completely and automatically, or that an external tight clock could be the solution. In my setup I have observed time-shifted clips, midi and audio, many times including the AK and AR.
There is some timing improvement, if background tasks like WLAN, Bluetooth, downloads etc. are disabled. And get all “buffers” as small as possible. There is a Driver-Error-Compensation lesson in the help files and Knowledge Base that explains how to test your environment and optimize the buffer sizes.