Tuvok didn't get his promotion until the 4th season. However, in the episode "Fury", when Kes goes back to the past when Voyager pretty much just entered the Delta quadrant...if you look at Tuvok's collar (most noticeable in conference room) you can see the Lt. Commander pips (3 pips). At that time he should only have the two pips for Lieutenant.
If you notice the first couple seasons of Voyager, Tuvok was wearing Lt. Commander's insignia (2 gold and 1 black pip) yet was called lieutenant. They changed his rank I think in the third season and then finally promoted him.