In Higgs context, do false vacuum hypothesis imply that true vacuum is *higher* (not lower)?

In theories of false vacuum for Higgs potential, the Higgs field would be currently in an instable false vacuum and would later evolve in a true vacuum, with a lower potential value.

Would this true vacuum be necessary characterized by a higher value of the Higgs field?

I would expect so, since in this hypothetic theory, at the early universe, the Higgs field was 0, so I would not see how the true vacuum value of field could be lower to the current value of vaccum, else in the Higgs field evolution towards the false vacuum, the field would have already encountered the "true vacuum", so it could not evolve to a false vacuum that has a field value higher to the true vacuum.

If so, why do theories of false vacuum give in their schematic a true vacuum lower (at the left) to the false vacuum: this looks impossible in the scenario of evolution of universe.

https://en.wikipedia.org/wiki/False_vacuum