Whether you use private addresses such as 10.10.10.0/24 or public addresses such as 22.214.171.124/24, it will make no difference in the actual configuration. For the purposes of this lab, a private address range was chosen, but if you like, in your GNS3 lab, or in your home lab, you can use public addresses as well.
In the real world, how you would configure this depends upon the way in which you connect to the Internet. In some cases, the E0/1 interfaces of the ASAs would be assigned a static public IP address provided to you by the ISP. In others, the ISP may provide you with some termination equipment such as a modem, a router, or a switch to which you must connect your ASA. That termination equipment may have a static or a dynamic public IP address. In such a case you may still be assigned a private address on your ASA, and may have to traverse NAT or some other translation service at your network edge.
In order to make this work, however, you will require to have a static routable IP address on at least one end of the link.
How you will end up creating the link will depend upon the topology of the edge of your network. There are various ways to deal with these scenarios, but for the purpose of this lab, the idea was to understand the configuration of the ASAs for a site to site IPsec VPN.
I hope this has been helpful!