Triangles don't follow the vertices changed on mesh

It's been while I've worked with mesh editing. And there is this little weird issue I've never encountered before.

I am changing vertices on the mesh, for the test, i am moving one vertex in some direction. The vertex moves like it should, but only one of the triangles moves with it, shouldn't all the triangles who connect to this vertex follow up too? At first i though that the imported mesh i've been working on has vertices separated, but it's not.

Here's a test with default unity cube, i am moving only vertices[0], as you can see only one triangle follow up, why not the rest of them?