What does work is "time" instead of "time_hires". Since I have no idea what values are available (I guess the table names?) and time only has a 1 sec resolution, what is a correct version of time_hires?
To answer my own question:
with modparam("acc", "time_mode", 2) and modparam("db_redis", "keys", "acc=entry:callid,time_attr&cid:callid") you'd get a millisec resolution timer in the key for redis