There is certainty in history and there is certainty in this case: The idea holds no merit whatsoever.

From an older answer:

There is no merit in this. The idea that Tito was a Russian agent or an Austrian Jew was something that – like so many things about Tito – its origins in the Second World War and has been advanced over time resting on either a very skewed way of viewing Yugoslavia or a right-wing agenda.

Like with so many leaders of political movements engaging in a guerilla war, when Tito entered the world stage during WWII, he was very concerned about his identity being discovered, hence also the name Tito. Early proclamations and communication with the Western Allies from 1941 for example are signed T.T. instead of Tito and according to Walter Roberts' still excellent book "Tito, Mihailovic and the Allies", the Western Allied governments had no idea who Tito was until 1943.

Since the war in the Balkans were a war of national liberation as well as civil war, the Partisans' enemies had a vested interesting in portraying the leader of the Partisans as a foreign agent or – in case of the Axis, Ustasha, and some Chetnik groups not aligned with Mihailovic – as a Jew, since as was evident from their own actions, they saw communism as puppet of the international Jewish conspiracy.

As far as can be told, first "concerns" about Tito's accent were raised by the Mihailovic Chentniks after Mihailovic and Tito had met in the fall of 1941 to iron out their differences. During that time, Mihailovic Chentniks and Partisans had a vertiable political conflict on their hands and were vying for support from the population. In light of the horrific German reprisal policy, the Mihailovic Chetniks wanted to pursue a policy of not provoking the Germans and rather building up until an Allied Balkan front could be opened akin to the Saloniki Front of WWI. The Partisans on the other hand opted for a policy of active attack, reprisals be damned, because they felt, the more cruel the Germans, the more the population would support the uprising.

While Mihalovic's Chetniks were far from an ideologically homogeneous groups, they were Serbian nationalists in the broadest sense. The Partisans on the other hand did include every Yugoslav nationality among their ranks. As part of a propaganda effort to show that they as Chentiks were the only people with the "real" interests of Yugoslavia in mind, Tito was painted as a Russian agent. With Tito's background as a professional comintern revolutionary this was easy but they also argued that even Tito himself was not really a Yugoslav and used his accent as an example. Aware of this, Tito was very careful thorough WWII and even into his official reign to hide that he had fought with the Habsburg armies in Russia and speculation about that gave further rise to this conspiracy theory.

In the West, the issue was once raised by the American secret services. There is an undated NSA report that asks the question if Tito was really Yugoslav and that deals with his accent. However, the problem with that report becomes clear because while they conclude that the accent might sound a bit strange, they also write that their biggest piece of evidence is Tito's impartiality with dealing with the different nationalities in Yugoslavia and therefore he can't be a real Yugoslav.

This is a stupid idea to put it mildly. Far from understanding the ideological commitment of Yugoslav communists in treating the various nationalities on a somewhat equal footing, it fundamentally misunderstands the real politik of the Tito regime where at least the appearance of treating the various republics impartial and equal was a huge source of legitimacy for political power – something Tito understood.

With the rise of post- Yugoslav nationalism, the idea of Tito being a non-Yughoslav gained traction again, mainly due to the fact that for the various hardcore nationalists, it fitted their narrative of Yugoslavia as their prison when it really should have been a vehicle for Serbian / Croatian / etc. hegemony. Especially in Croatia, where Tito was from, the idea that a Croatian could have been responsible for Yugoslavia appalled ultra-nationalist circles and with the reemergence of the Neo-Ustasha movement, they concluded that because he was a communist, he must have been a Jew; an Austrian one at that. It's basically an anti-Semitic conspiracy theory, which aims at pointing your enemies, even when dead as Jews or Russian agents, which in the mind of the peddlers of this theory amounts to the same thing.

As for the accent, which is the only thing where people can make even a half-hearted argument since for everything else historical documentation just doesn't exist: When dealing with the Yugoslav language, we encounter such a variety in how it is spoken, that today, it is counted as four strongly different variations of one language: Serbian, Croatian, Bosnian, and Montenegrin. It varies strongly between the coastal areas and the inland areas, has two alphabets, and has three major dialect groups (Štokavian, Kajkavian and Chakavian) that split into a variety of sub-groups again. Additonally, with many a marriage including people speaking different dialects or even languages (Tito's father was Croatian and Tito's mother a Slovene) coupled with a long time spent abroad and having learned German as well as Russian, a peculiar sounding dialect is something that is in fact very Yugoslav.

In conclusion, the idea that Tito was not Yugoslav but a Russian agent or a Jew is a conspiracy theory popular in extreme right-wing circles because it fits their world view nicely and has no historical validity whatsoever.