I do the semi tuck sometimes. It only works with low-rise jeans and a casual, fitted, cotton jersey knit top of exactly the right length. To my eye it doesn't work with a dressier outfit, with higher-waisted jeans or even a casual skirt.
The reason I do the semi tuck is that when you wear a belt (which I often need to do to prevent jean slide-down) , the buckle leaves a big lump under your shirt. Tucking your top to display to the buckle gets around this, but the top has to be a little clingy. A looser, woven shirt or blouse tucked in front and flapping around at the back looks funny, to be sure.
This issue ties right in with one of the reasons I joined this forum. I had been having problems with jean slide-down, and joined so I could ask advice about how to prevent this without wearing a belt. Someone (I can't remember who) suggested wearing a slim belt and sliding the buckle over to your hip to avoid the unsightly belt-buckle lump. I tried it, and it works! So I'd like to give credit where credit is due -- whoever you are, thanks for the tip! I do the semi-tuck a lot less often now that I have that trick up my sleeve.