Fetch just inserted data in master/slave model?
This is often handled by the application actively choosing to read from the master based on context.

A common example I've seen mentioned is a database of blog posts.  *Viewing, a blog post would obviously be done from a replica, but previewing an edit to a blog post -- which may be the same code, since it's rendering the post -- might be something you do by reading from the master.

Depending on the application, you might also read from the replica and then fall back to reading from the master if you don't find what you expect.

There are also solutions, like Maxscale -- designed by MariaDB but works with MySQL too -- that are essentially a proxy between your app and both MySQL servers.  Whenever you are in a transaction, you're talking to the master, whenever you're not in a transaction and issue a SELECT, the queries go to the replica... so you can easily force a read from the master just by doing it in a transaction.  There are other rules in play as well that send certain statements to both servers, such as USE and SET statements.  If the replica lag goes beyond a certain threshold, Maxscale sends everything to the master.