Direct proof of use
The Tornado-G is documented in the 2011 Syrian Civil War through Russian official statements reported on December 17, 2018. Interfax reported that Deputy Prime Minister Yury Borisov, after a trip to Syria, said the Iskander-M missile system and the Tornado-G and Smerch multiple rocket launchers had confirmed their effectiveness during Russian combat operations in Syria.
Missile Threat at the Center for Strategic and International Studies summarized the same statement the next day, writing that Borisov confirmed use of the Tornado-G and Smerch multiple launch rocket systems along with Iskander-M and air-defense systems in Syria. The Moscow Times likewise reported that Borisov said Russia had tested Tornado-G and Smerch launchers in Syria.
Sources: Interfax Iskander-M Syria, CSIS Missile Threat Syria, Moscow Times Syria Weapons
Timeline
Russia entered the Syrian war on the side of the Syrian government in September 2015. The public Tornado-G record does not show a dated first strike or a named launch unit, but the December 2018 Borisov statement places the system inside Russia's Syria combat experience before or by that date.
Russian government newspaper Rossiyskaya Gazeta reported the same day that Tornado-G and Smerch multiple rocket launchers had confirmed their effectiveness in Syria and connected Borisov's remarks to a broader Russian review of weapons used in the campaign.
Sources: Moscow Times Syria Weapons, Rossiyskaya Gazeta Syria Weapons
Operational role
The available sources support a fire-support role for Tornado-G in the pro-government coalition, rather than a transfer to a separate Syrian unit or a named Syrian battlefield incident. The parent weapon is a 122 mm multiple launch rocket system, and Rosoboronexport describes Tornado-G as intended for destroying enemy manpower, armor, artillery and mortar batteries, command posts, and other targets.
The public record should therefore be read narrowly: sources support Russian campaign use or combat testing of Tornado-G in Syria, but they do not establish where the launcher fired, which formation operated it, what munitions were fired, or what effects any strike produced.
Sources: Interfax Iskander-M Syria, 122mm Tornado-G MLRS