I guess your misstake is that use the pipe symbol which is not necessary. Also you download from localhost which is the localhost of each server itself.
So try this:
#!/bin/bash
declare -a _servers=('192.168.1.1' '192.168.1.2' '192.168.1.3' '192.168.1.4')
ORIGIN = "192.168.1.254"
for ((i=0;i<${#_servers[@]};i++));
do
echo "-------- Server: ${_servers[i]} ---------"
ssh myUser@${_servers[i]} wget http://${ORIGIN}:8080/someDirectory/refreshSomePage.jsp
echo "-------- Complete ---------"
done
I just hope that you use a ssh key based authorization to avoid any future inputs.