Yep, what you hear in that demo is all done by the pedal, I didn't use the trem bar at all, at slow speeds the Vibrato mode tends to sound a bit seasick-ish, but it starts to sound a bit more like a vibrato effect as you turn up the effect speed, the other mode, Chorus, is actually a Phaser effect meant to replicate the sound you get when playing through a Leslie Rotating Speaker, you'll notice that the effect becomes more prominent as the speed of the effect increases, this is normal behaviour and original Univibes behaved that way too.
Jimi Hendrix most likely used the Univibe on some songs he recorded in the Band Of Gypsys to give his guitar a kind of underwater-like sound.
A good example is his song "Machine Gun".