No, there's no AJAX in the code you posted.
Master pages and content pages are entirely server-side concepts. The client (browser) has no knowledge of them. The server-side code (the ASP.NET Framework in this case) assembles components when responding to a request, building an output stream to send to the client.
In this case that assembling of components includes executing the server-side code, "merging" the master page and content page, interpreting the various server-side controls and data bound to them into client-side HTML/JavaScript, and building one big string to send to the client as the rendered HTML.
It does this on every request for a page. When you open the page in your browser, go to View Source to see the "string" that was output from the server-side code. You'll see that it's all one page, there's no client-side distinction between master pages and content pages.