Before you can connect WP Email Manager with myVesta, you first have to add your server’s IP to myVesta’s API whitelist IPs if your WordPress install is on a different/remote server.
To do so, please follow these steps that are are copied from this forum article:
In SSH console run:
mkdir -p /usr/local/vesta/conf_web
pub_ip=$(curl -s vestacp.com/what-is-my-ip/)
local_ip=$(ip addr|grep 'inet '|grep global|head -n1|awk '{print $2}'|cut -f1 -d/)
echo "$pub_ip" > /usr/local/vesta/conf_web/allow_ip_for_api.conf
if [ "$pub_ip" != "$local_ip" ]; then echo "$local_ip" >> /usr/local/vesta/conf_web/allow_ip_for_api.conf; fi
echo "127.0.0.1" >> /usr/local/vesta/conf_web/allow_ip_for_api.conf
and add to /usr/local/vesta/conf_web/allow_ip_for_api.conf any other IP that should be able to access the  API on that server.
You can add each IP per each line.