do you really need an array
bash
$ ipAddress="10.78.90.137;10.78.90.149"
$ IFS=";"
$ set -- $ipAddress
$ echo $1
10.78.90.137
$ echo $2
10.78.90.149
$ unset IFS
$ echo $@ #this is "array"
if you want to put into array
$ a=( $@ )
$ echo ${a[0]}
10.78.90.137
$ echo ${a[1]}
10.78.90.149
@OP, regarding your method: set your IFS to a space
$ IFS=" "
$ n=( $(grep -i ipaddress file | cut -d'=' -f2 | tr ';' ' ' | sed 's/"//g' ) )
$ echo ${n[1]}
10.78.90.149
$ echo ${n[0]}
10.78.90.137
$ unset IFS
Also, there is no need to use so many tools. you can just use awk, or simply the bash shell
#!/bin/bash
declare -a arr
while IFS="=" read -r caption addresses
do
case "$caption" in
ipAddress*)
addresses=${addresses//[\"]/}
arr=( ${arr[@]} ${addresses//;/ } )
esac
done < "file"
echo ${arr[@]}
output
$ more file
foo
bar
ipAddress="10.78.91.138;10.78.90.150;10.77.1.101"
foo1
ipAddress="10.78.90.137;10.78.90.149"
bar1
$./shell.sh
10.78.91.138 10.78.90.150 10.77.1.101 10.78.90.137 10.78.90.149
gawk
$ n=( $(gawk -F"=" '/ipAddress/{gsub(/\"/,"",$2);gsub(/;/," ",$2) ;printf $2" "}' file) )
$ echo ${n[@]}
10.78.91.138 10.78.90.150 10.77.1.101 10.78.90.137 10.78.90.149