The home city of Ukraine's Eurovision act was hit by Russian missiles moments before the band took to the stage in Liverpool, reports say.
The chief of the regional state administration, Volodymyr Trush, confirmed two people had been injured.
Ternopil mayor Serhiy Nadal confirmed warehouses were damaged.
Ten minutes before taking to the stage at the Liverpool Arena, Tvorchi posted on Instagram citing reports of Ternopil in western Ukraine being attacked.
After performing, Tvorchi wrote again on Instagram saying: "Ternopil is the name of our hometown, which was bombed by Russia while we sang on the Eurovision stage about our steel hearts, indomitability and will.
"This is a message for all cities of Ukraine that are shelled every day. Kharkiv, Dnipro, Khmelnytskyi, Kyiv, Zaporizhzhia, Uman, Sumy, Poltava, Vinnytsia, Odesa, Mykolaiv, Chernihiv, Kherson and all others.
"Europe, unite against evil for the sake of peace!"
The UK's ambassador to Ukraine Dame Melinda Simmons described Tvorchi's Eurovision performance as "poignant".
Writing on Twitter, she added: "Reminder that the reason why Ukraine could not host this event is because Russia continues to invade and the people of Ukraine live in continuing danger."