From my classes I don't hear about a lot of italian mathematicians, but two of them, Fubini and Tonelli, are both related to multivariable calculus. Is there a reason for this? Just a coincidence? Or was Italy historically stronger in this area?
In a way, but not exactly. From about the same period (late 19th-early 20th century), the names of Peano (differential equations, mathematical logic), Betti (algebraic topology, elasticity theory), Veronese (classical geometry), Castelnuovo, Enriques (algebraic geometry), Beltrami, Bianchi, Ricci-Curbastro, Levi-Civita (Riemannian geometry, tensor calculus), Arzela, Cesaro, Dini, Vitali (mathematical analysis), Volterra (integral equations, mathematical biology) are pretty widely known. Of course, Cavalieri and Torricelli were early calculus pioneers, and both Riemannian geometry and analysis are sophisticated descendants of calculus.
According to Mathematicians in Bologna 1861–1960, p.469, "the collaboration between Betti and Brioschi was the true driving force behind the initial development of Italian mathematics". Betti befriended Riemann, and did a lot to promote his ideas in Italy. He also deserves a lot of credit for fostering top grade mathematicians, both geometers and analysts. Six of the above were his doctoral students (Arzela, Bianchi, Dini, Enriques, Ricci-Curbastro and Volterra), see his Mathematics Genealogy page. Tonelli was Arzela's student, and Fubini was both Dini's and Bianchi's. Cesàro's 1890-s textbooks also promoted both subjects. Brioschi founded Milan's Polytechnic in 1863, geometers Cremona and Beltrami were his students. Beltrami was also active in promoting Riemann's ideas, he translated his works into Italian.