Transnistria is one of the many de facto independent states that came out of the dissolution of the Soviet Union, and in comparison to the three in the Caucasus, it is the one I am least familiar with. However I can give some information.
Most of Moldova was only incorporated into the USSR in 1940, when as part of the pact with Nazi Germany, the Soviets annexed parts of Romania (Bessarabia and Bukhovina). Up to this point there had been a Moldavian ASSR (autonomous republic, part of the Ukrainian SSR), which had a plurality (45% or so) of ethnic Ukrainians, followed by Moldavians/Romanians (30%). It also largely consisted of modern Transnistria, but not the rest of Moldova.
The annexation of the Romanian territories, or re-annexation as may be the case, as it was part of the Russian Empire for about a century until the Revolution, altered the territorial and ethnic composition of the region. A large swatch of ethnic Romanians were added, and the Moldavian ASSR was upgraded to a full Soviet Republic (SSR) to deal with it. This was how it lasted until the fall of the Soviet Union, and I'll note that while I don't have statistics for the interim, the ethnic Romanian/Moldovan population became a majority by 1989, while the Ukrainians/Russians went down to 45% or so.
Like the other regions, glasnost and perestroika allowed grievances to be aired, so the ethnic minority, in this case Slavs(which was unique for the Soviet Union) to complain that they were discriminated against by Romanians/Moldovans (which are really the same people, except for a border, but that's not the point here). It didn't help that pro-Romanian groups were becoming more active and demanding more action towards promoting their identity, with some even calling for the region to rejoin Romania. When the Popular Front, the leader of these groups, won elections in 1990 to form the government in Moldova, Transnistria moved to secede, fearing they'd lose all their rights.
With the Soviet/Russian 14th Army stationed in Transnistria, and largely composed of locals, and support from various Cossack groups who wanted to help their fellow Slavs, a brief war broke out, with a ceasefire signed in 1992 that has left the region as a de facto Soviet republic.