Process substitution with tee and paste

The reason you are seeing the output of the original command is because tee outputs to stdout as well as the files specified. To discard this you can put >/dev/null at the end of the command or redirect this output to one of your process substitutions by adding an extra >, eg:

command | tee >(sed -rn 's/.*foo (bar).*/1/p') > >(awk '{print $3}')

Or simpler just use another pipe:

command | tee >(sed -rn 's/.*foo (bar).*/1/p') | awk '{print $3}'

As for combining the result of the two process substitutions using paste, unless there is some obscure shell trick that I don't know about, there is no way to do this without using a named pipe. Ultimately this is two lines (formatted to more for clarity):

mkfifo /tmp/myfifo
command |
  tee >(sed -rn 's/.*foo (bar).*/1/p' >/tmp/myfifo) |
  awk '{print $3}' |
  paste /tmp/myfifo -

If you are putting this in a script, also consider using the recommendations for creating a temporary named pipe here.

You can do all of that just in sed.

command | 
sed '/\([^ ][^ ]*  *\)\{2\}/{h
         s///;s/^  *//;s/ .*/p
     g};s/.*foo \(bar\).*/\1/p;d'  

But as to the other thing, you have tee around the |pipe files:

cmd1 | {     
    {   tee /dev/fd/3 | 
        cmd2 >&2
    } 3>&1 | 
    cmd3
} 2>&1 |paste

But since you're already using sed you can use it like a smart tee and only dup/redirect when you have to:

cmd | { 
    sed -n 'p;s/.*foo \(bar\).*/\1/w /dev/fd/3' |
    awk ...
} 2>&1