Symmety weirdness

In short - I joined to objects  into one and symmetry seems to be wrong. I want to ask you is it just how vw work or bug?
See image in attachment for  detailed description.
Is seems it is not consistent is symmetry calculated from mesh pivot, object pivot or something else. Also if it is calculated from mesh pivot, then is there a way to change mesh pivot?

Second attachment  is example of merged objects: gray orginal mesh, red second mesh, green - bridged face to join meshes.

Jose: The symmetry plane is mesh pivot based, not object pivot. You can adjust mesh pivot by adjusting object pivot with option which will move both object pivot and mesh pivot together. object pivot tools are available in both visual tool and streamline tool. You can also adjust mesh pivot alone in hierarchy mode.

Symmetry plane can be set through Edit > Options > Shortcut Symmetry Options.

Symmetry plane can be viewed by View > Show Symmetry plane. If the object is symmetrized, the used symmetry plane will present. Otherwise the choice symmetry plane set through options will present, and this is the one take effect when you hit Ctrl + Q.

Thanks Istonia. I didn't noticed mesh pivot transform, under object pivot tolls.
So I turned on "Display symmetry plane" and it shows me two of them. See in attachment.
Is this bug?

I think you have two meshes. That's why there are two symmetry planes. You can check this in mesh List tool under Mesh mode.

You are right, there were 2 meshes. For second I thought that 2 meshes that I joined and bridged into one were not updated as one mesh, but I forgot I had third one mesh - bottom one, and not visible here.