At the end of March  Nakaznoy Hetman Ostap Gogol with the Podolian Regiment and some Budjak Tatars invaded the Letichevsky Powiat of the Podolian Voyevodstvo. Cossack-Tatar troops looted and burned the neighborhood of Bar, Medzebozh, Derazhnya, Old and New Senyavy, Zinkov and Gusyatin. On 20 July Doroshenko resumed the siege of the Polish garrison at Bila Tserkva and sent his younger brother Gregory and 2,000 Cossacks to Podolia. He sent the Kalnitsky regiment to Crimea to help Adil Giray against Zaporozhians. Doroshenko, with no more than 5,000-8,000 Cossacks  and 5,000-6,000 Tatar allies did not dare to go to war, but awaited Adil Giray before starting an offensive against Commonwealth. Most of the Budjak Mirzas who were with Gregory Doroshenko, on learning of the approach of the Polish militia, hastily left their ally and returned to their camps. Grand Crown Hetman Jan Sobieski advanced against Doroshenko and the Crimean horde. On 26 August at Bratslav the Polish army routed the Cossack and Tartar troops. The Poles defeated the Budjak Tatars and burst into Bratslav. The Cossacks took refuge in the city castle and the broken Tatars began to retreat in panic. Sobieski led cavalry in pursuit of the Tatars while some Poles stayed in Bratslav to besiege the castle. The Poles followed the Tatars to Batorg and completely defeated them. The Cossacks in the castle learned of the defeat of the Tatars and surrendered. Emir Ali, who commanded the Budjak troops said he lost 500 men. Despite the victory, Sobieski withdrew to Bar, where he arrived on 30 August.

Answer this question based on the article: Which happened first, the Kalnitsky regiment being sent to Crimea or the Poles defeating the Budjak Tatars?
Kalnitsky regiment to Crimea