The tip of the tongue is vibrating. Try puffing an “H” sound with your mouth slightly open several times. Then you need to get the front part of your tongue to vibrate just below and against the top of your mouth. Practice this without using the melodica until you get the feel of it. You may find it easier to get the sound without a mouthpiece and easier with some mouthpieces than others. I think this is what you’re looking for, but someone else can probably get closer or offer clearer instructions. You’re not doing the vibrating with the muscles of your tongue, you are positioning the tongue in such a way that the air vibrates it.
I strongly recommend that you listen to recent sound samples posted by Quetscher and see posts by jazzman1945 (Search “The Amazing Melodica”) and Lowboy Bootay describing different techniques. Lots of sound samples also by Lowboy. Quite a lot can be learned by trying to imitate what you’re hearing — recorded music also, but especially these demonstrations by skilled players who are sharing sound samples.