Does wsrep_cluster_address only accept the intranet IPs? I was installing Percona XtraDB Cluster with 3 nodes.

Each node has a unique Internet IP address.

Following the docs Quick Start Guide for Percona XtraDB Cluster, I got the first node running but failed to get the other two nodes working.

So I am doubting that the wsrep_cluster_address only accepts the intranet IPs, is that true?
You can use any IP address in wsrep_cluster_address (you can use hostnames too). You need to make sure that all ports required are open for Galera communication (3306, 4444, 4567, 4568). There are many other reasons for "failed to get the other two working" so log files would be very helpful.