Do all plants of the salvia genus originate in the Western Hemisphere?

There are several species of Salvia that grow in Europe, Asia, and
Africa:

"Sage, otherwise known by the genus name Salvia, has become extremely
popular in low water use landscapes throughout the Southwest. Their
brilliant colors, along with the various shapes and textures, make
them particularly useful in area landscapes.

The many species in current use today come from various parts of the
world, including Mexico, South America, Europe, Asia, and Africa..."

http://ag.arizona.edu/pinal/horticulture/homehorticulture/currentissues/groundcovers/salvia/

Several European, African and Asian species are mentioned here:

http://www.seedhunt.com/salvia.htm

Turkey is accepted to be the primary or the secondary genetic center
for some plant groups at the level of genus or species. The following
are among the genera whose genetic center is considered to be in
Turkey: Achillea, Allium, Astragalus, Centaurea, Draba, Iris, Salvia,
Verbascum
http://www.mfa.gov.tr/grupc/ca/caa/uu/e1010.htm

I guess they all began growing somewhere, but it could be before
humans had any influence.