Searched the internet for hours, I couldn't find a tutorial for making a movable mouth marionettes. Is it a professional's secret thing?

There is some stuff out there, but I'll admit, getting good clear specifics on puppet mechanisms can be a challenge. You might alter your search for the mechanics of vent figures (for ventriloquists) and then see if there's a way to adapt what you find to fit a marionette. Every puppet maker uses different techniques, which makes it a challenge.

Chris is right you will have a lot more luck searching for "moving mouth mechanisms for ventriloquist dummies".  Look at the image search results.  Same concept except that instead of attaching a string or trigger that pulls down you are running your string up to the control.

The basics are that you have a "hinge" at the back of the mouth piece in the same place you would have your hinge for a hand in mouth puppet. I normally used gravity instead of a spring to keep the mouth closed by running an extension form the hinge back about 1/2 to 1 inch and then putting lead weight on it. I attached the string to this extension where the weight was and the ran it up through the head. Pull up on string and the mouth opens. Release string and the weight pulls it closed.  Once you see some of the images it will make a lot more sense.

Found a page over at Puppets and Props that give you a nice simple explanation of a vent dummy mouth. http://www.puppetsandprops.com/Mechanics.html Again same concept only you go up instead of down with the control string.

Thanks very much Shawn and Chris, I haven't thought in that direction