The overall impression I got from reading a multitude of memoirs and personal accounts, is that it was not nearly as bad as being occupied by Germans. Firstly, a significant part of the Romanian-occupied territory, namely Bessarabia, was Romanophonic already, and they treated the Bessarabians, and even the Turkish but Russian-speaking Gagauz, very favorably.
Odessa, the biggest single city in the Romanian zone of occupation, did not begin to suffer any real ill effects, namely the wholesale murder and deportation of Jews, until Romanian control was replaced by German. There are several examples of Romanian authorities both passively and actively resisting German orders to round up Jews and other undesirables. In fact, several accounts I ran across none too subtly suggest that a black market trade blossomed in Romanian-controlled Odessa, which is not surprising given that the two groups we're already well familiar with each other through centuries of geographic proximity and where no real ethnic or even politically based enmity existed.
This is not to say that there were no bad episodes. As with any case where armed men of one nation find themselves among the conquered civilian population of another, there were rapes, murders, forcible seizure of property and the like. But on balance the population did not suffer nearly as much as other Soviet citizens did under German occupation.