It’s a Russia-backed puppet state, the same as Abkhazia (same period of time), South Ossetia (2008), or a newer DNR/LNR (2014). It’s not people that decided to do something, it’s that big pile of shit country making life worse for them.
Most of the people in Transnistria very much value their independent status, it allows them a degree of practical freedom in commerce that they would not have otherwise. They also typically are not limited by the nation's independent status as they also nearly universally hold Ukrainian or Moldovan citizenship in addition to Transnistrian.
Furthermore, the practical matter of it is that the PMR (Transnistria) military cannot hope to withstand say, a prolonged assault with the Ukrainian military. Though both Ukraine and Moldova officially declare Transnistria illegitimate and their rightful clay, extremely prominent and well connected people in both countries also greatly benefit from its existence. Lots of border and jurisdictional games to play. Nobody seriously wants it to go away.
A very abridged version is that Transnistria independence is a result of war between two factions, and neither of them hold the moral high ground. After the fall of USSR in 1991 Moldovan nationalism became stronger and pushed for pro-Moldavian and pro-Romanian views even in the regions of that were historically dominated by Russian and Ukrainian population. Local population rebelled against that, and Russian state used this conflict to their advantage using 14th army, stationed there.
On a side note, Ukrainian and Russian nationalist volunteers also came to assistance of Transnistria against Moldova. Some of those people were fighting on the same side in 1992 only to be fighting against each other in 2014.
And here I stop. Because this scenario (ethnic minority region in a conflict with the rest of country) has happened multiple times in the history. Rarely one side is 100% right or wrong.
I don’t know about Kosovo, but I know for sure about DNR. Transnistria is a crappy corruptionist hole for money laundering, there is nothing about people’s will there as well.
Also, Ukrainian propaganda does not exist. It’s more of a for-hire services that work for whomever pays more, not for the state itself. It’s one of the reasons why shit like that happens, since there is no state-backed push against Russian agenda.