Problem with phpmyadmin after

You have only one phpmyadmin installation if you follow my recommendation and phpmyadmin offers all servers at login, so no need to switch the link to different servers.

Take a look at the phpmyadmin config file and add all your servers there, after you did that you will see that phpmyadmin offers a server selector automatically.

Installing phpmyadmin on the db servers is not a good idea as this would require you to install apache on these servers as well which consumes server resources without giving you any benefits.