This is because an AJAX request is calling a POST method. Change the AJAX request to GET or probably better just use HTTP Fox to determine the ajax request URL

Let’s say the url is See the directory structure of / module/controller /action? That is the module / controller / action and determines the page path that is used for the rule.

Next, create a rule telling the page cache to ignore the post request. In this case the rule would be this: <module-controller-action><on_post/></ module-controller-action>

Now, go to Page Cache -> Configure -> Advanced -> Page Rules and add this rule and save.

What this rule does is tell the page cache to ignore the post requests for that particular module/controller/action. 

You can also enable the output headers in Page Cache -> Configure -> Developer and look at the HTTP Headers for the AJAC request. The “X-Page-Path” header will be what you need to use for the rule (in this case namespace-module-action would be the page path).