Usually intarsia is knitted in stockinette stitch (every front side stitch is knit, every back side stitch is purled). In most cases it's not neccessary to make a beautiful or reversable back side when knitting stockinette stitch because you will not see it anyway. That is why it's possible to just twist the yarns at the transition points and go on. This is totally adaptable to garter stitch intarsia IF you knit straight lines and no diagonal patterns.
It all get's complicated if you want to to the diagonal lines. If you use the twisting only the backside will look untidy at the back side when leaningto the left and on the front side when leaning to the right. This is caused mainly because of the nature of the purl stitch. If you work a knit stitch over a purled one in two different colors you will see, that the line......
For some of my handpuppets it's neccessary to knit intarsia in the round. Intarsia is a colourwork technique where the yarn is not floated in the back of the knitting as in fairisle techniques, but each section is knit with it's own thread. Intarsia is often used where the pattern calls for bigger sections in one colour when stranded knitting would create a thick fabric.
Usually intarsia is knitted flat. Knitting back and forth you always have the threads in the direction you want to have it. When knitting in the round you knit in one direction only. So here is the problem. Given you have 2 sections and knit section 1 and 2 and want to continue with section number 1, the thread of section number 1 is still at the end of the section - not where you need it.
In fact you can't knit intarsia in the round UNLESS......