Matija married Tea Budimir, a physiotherapist, in 2016 and has a child named Marko.[4][7] He is from Rijeka on the Kvarner Gulf and currently lives in Croatia's capital city, Zagreb.[5] He completes most of his training on the Sava River in his home town but spends a significant proportion of his time at the Tacen Whitewater Course in nearby Ljubljana,[8] making it somewhat of a home course for him and other Croatian slalom canoeists.[9]
In 2008 Matija made the finals at both junior international events, finishing 10th at the Europeans (after incurring a 50-second penalty) and 6th at the Worlds.[12][13] During this time he also competed at the U23 level, finishing 8th in C1 team at the Europeans in 2007 and 2008.[14] Matija competed in several World Cups as a Junior and achieved a 15th place at the 2008 event on his "home" course in Tacen.[15]
Marinić finished in 42nd place at the 2015 World Championships in Lee Valley which doubled as a qualification event for the 2016 Summer Olympics, missing out on automatic qualification. His only other chance to qualify was at the 2016 European Championships in Liptovský Mikuláš. Matija finished in 11th place at this event, just short of the top ten and the opportunity to race Ander Elosegi for the European quota.[20]
Matija has dealt with knee issues since he was 18, due to the awkward sitting position required for C1. Following the announcement of the postponement of the 2020 Games, he underwent knee surgery so as to not be held back by his injury and to be "faster and better" at the delayed 2021 Games.[7] Marinić spent the winter leading into the Olympics training at Wadi Adventure in the United Arab Emirates with fellow Croatian Ren Korpes.[22] In the lead-up to the postponed Games he won an ICF World Ranking race in April in Tacen,[9] and made the final of the 2021 Canoe Slalom World Cup in Prague, where he finished in third place but was disqualified for a delayed start.[23]
On 13 July 2021, 8 days after arriving in Tokyo to prepare for the 2020 Summer Olympics, Matija and coach Stjepan were sent into self-isolation by the Olympic organisers due to there being an infected passenger on their flight.[24] They were initially required to self-isolate for a week but were allowed to return to training on the 15 July, two days later, following an appeal by the president of the Croatian Olympic CommitteeZlatko Mateša.[25] Mateša publicly criticized the handling of the issue, calling it a "glaring example of the inability of the organizers to deal with the problems associated with the pandemic".[26]
Matija finished in 11th place in the C1 event at the 2020 Games, after being eliminated in the semi-final.[6]
Notes a No overall rankings were determined by the ICF, with only two races possible due to the COVID-19 pandemic. b Marinić finished 3rd but was disqualified from the final, being classified 10th.