Here is a wrapper script that should do what you want.  I can't confirm that it works on AIX ksh, but it works using sh (AT&T Research) 93u+ 2012-08-01 (Debian's ksh package calls it the "Real, AT&T version of the Korn shell."  This is intentionally neither pdksh nor its mksh fork).
This is portable and should work in all POSIX shells.
pipe1+2.ksh
#!/bin/ksh
touch err.log here.log      # create the logs now so tail -f doesn't complain
tail -f here.log &          # follow the output we'll pipe to later (run in bg)
HERE=$!                     # save the process ID of this backgrounded process
tail -f err.log >&2 &       # follow output (as above), pipe output to stderr
ERR=$!                      # save the process ID
"$@" > here.log 2> err.log  # run given command and pipe stdout and stderr
RET=$?                      # save return value
sleep 1                     # tail polls at 1/s, so wait one second
kill $HERE $ERR             # stop following those logs
exit $RET                   # restore the exit code from given command
So you invoke it as pipe1+2.ksh shell.ksh (assuming both commands are in your path).
Here's a test version of shell.ksh:
#!/bin/ksh
echo this output is stdout 1
echo this output is stderr >&2
echo this output is stdout 2
and a trial run:
# ksh pipe1+2.ksh ksh shell.ksh
this output is stdout 1
this output is stdout 2
this output is stderr
# cat here.log
this output is stdout 1
this output is stdout 2
# cat err.log
this output is stderr
A note:  because tail -f isn't instantaneous, stdout vs stderr will be slightly out of order.  It won't even be consistent between runs, at least with code that runs as fast as echo.
I doubt your version of tail supports it, but GNU tail has a -s SECONDS flag that lets you specify a different polling interval as a decimal value, so you can try e.g. tail -f -s 0.01 … to improve the ordering of what is displayed.  If your version of sleep also supports decimal values, change it to match that number.
 
(I had originally crafted a complicated file descriptor piping response based on one of the "more elaborate combinations" in the amazing Csh Programming Considered Harmful, but that didn't seem to work.  See the comments and/or the initial version of this answer.)