I understand that Josip fought on the Eastern front during World War I, but did he partake in the fighting duringWWII or the Spanish Civil War?
Tito did take part in both the Spanish Civil War and WWII, although in both wars he had a role that didn't involve him in direct fighting. It's unlikely he ever fired a weapon towards the enemy in both wars.
Tito's role in the Spanish Civil War is actually the most obscure part of his biography. His official role was the one of a liaison between the Comintern, the leadership of the Communist Party of Yugoslavia (CPY) in exile in Paris and Yugoslav volunteers in International Brigades. In that role, he traveled to Spain at least two times - to Madrid in 1936 or 1937 and to Barcelona in 1938. It seems he actually wanted to join the International Brigades as a fighter, but the Yugoslav party leadership dissuaded him from doing so.
According to the excellent book by Jože Pirjevec Tito in tovariši, the reason why that chapter of Tito's life is so poorly documented is that his "liaison" function apparently included collaboration with NKVD in liquidating the "trotskyists" and other party opposition in Spain. Occasionally, there were accusations that he was involved in organizing military tribunals for "those who resisted the creeping GPU dictatorship that was organized in Spain in 1936-37". Those accusations can't be confirmed without a doubt, since the documents that would prove his involvement don't exist. On the other hand, according to Tito's close associates Vlado Dapčević and Anka Butorac, Tito did privately admit his status as a NKVD asset, and even told Butorac he had her boyfriend killed in Spain. Official Tito's biographies from the communist period in Yugoslavia simply glossed over that part of his career and instead focused on his contemporaneous struggle against factionalism in the Yugoslav party.
Tito became the General Secretary of the CPY in 1937. Accordingly, he was the undisputed leader of the partisan resistance movement in Yugoslavia since day one. From 16 September 1941 the partisan headquarters was constantly located on the liberated area and it was mobile until 1944, when it relocated to the island of Vis and then permanently to Belgrade after the liberation of the city. Thus he never took part in direct combat, since that is not a job for a supreme commander. However, he did come under enemy fire on two occasions:
On 9 June 1943, while the partisan main force was trying to break out of German encirclement in the Sutjeska canyon, a Luftwaffe aircraft managed to score a direct hit on the partisan staff. Tito's dog saved his life by throwing himself in front of Tito in the moment of explosion; nevertheless, Tito was wounded in the arm, making him the only allied supreme commander that was wounded in action during WWII.
The second time was on 25 May 1944, when German army execuded an airborne landing on Drvar, at that point the location of the partisan political and military leadership. The goal of the landing was to kill or capture Tito. Tito and his closest associates managed to sneak out of the cave where they were hiding, while being under constant enemy fire, and escape on foot to the safer area on the Stol mountain.
Source: Jože Pirjevec, Tito in tovariši, Cankarjeva založba, Ljubljana 2011, p. 47-49, 136-139, 163-168