Build a command dynamically

Don't try to make an executable string. Instead build the arguments in an array and use that when calling tar (you are already using an array properly for EXCLUDE):

#!/bin/bash

directory=/tmp

exclude=( "hello hello" "systemd*" "Temp*" )

# Now build the list of "--exclude" options from the exclude array:
for elem in "${exclude[@]}"; do
    exclude_opts+=( --exclude="$directory/$elem" )
done

# Run tar
tar -cz -f tmp.tar.gz "${exclude_opts[@]}" "$directory"

With /bin/sh:

#!/bin/sh

directory=/tmp

set -- "hello hello" "systemd*" "Temp*"

# Now build the list of "--exclude" options from the $@ array
# (overwriting the values in $@ while doing so)
for elem do
    set -- "$@" --exclude="$directory/$elem"
    shift
done

# Run tar
tar -cz -f tmp.tar.gz "$@" "$directory"

Note the quoting of $@ in the sh code and of both ${exclude[@]} and ${exclude_opts[@]} in the bash code. This ensures that the lists are expanded to individually quoted elements.

Related:

• How can we run a command stored in a variable?

mix(){
        p=$1; shift; q=$1; shift; c=
        i=1; for a; do c="$c $q \"\${$i}\""; i=$((i+1)); done
        eval "${p%\%*}$c${p#*\%}"
}
mix 'tar % -zcf tmp.tar.gz' --exclude "/tmp/hello hello" "/tmp/systemd*" "/tmp/Temp*"

EXCLUDE=("/tmp/hello hello" "/tmp/systemd*" "/tmp/Temp*")
mix 'tar % -zcf tmp.tar.gz' --exclude "${EXCLUDE[@]}"

Extending the answer here. This doesn't rely on any bashisms, it will also work fine with debian's /bin/sh, and with busybox.