When looking into the Automation Engine logs, user actions can be distinguished by a userID and session ID, for instance: 

01/131304.331 -          <?xml version="1.0" encoding="ISO-8859-15"?><uc-env clientVersion="11.2.9+build.1537849707208" redlight=" " request="prm_2682" session="0000000474921870" useridnr="0003424710">   <request name="getlicencelist" src="prm"/>...

How can we find back the user that did this action?

The WP logs or traces don't give any hint about the link between user and ID.
In the DB table AUSR, we can find information about currently logged users but not about past logins.

Release:
Component: AAUTEN

If you need to make the link between a user and session ID you can activate object audit and created a revision report that also shows me the Session ID. The revision report command would look something like this:

ucybdbrr.exe -B -C<client> -FUSER -OC:\Temp\report.txt -D1YYYYMMDDhhmmss -D2YYYYMMDDhhmmss
or
ucybdbrr.exe -B -C0022 -FUSER -OC:\Temp\report.txt -D120190405000000 -D220190405120000