It is crucial that you have the skill to play two consecutive notes in the same fret on adjacent strings. For example, try to play a C in the fourth fret on the 3rd string and follow it immediately with an E in the fourth fret on the 2nd string. If you use the same finger for fretting both notes, and you try to lift it off the 3rd string before pushing it down on the 2nd, not only are you going to be short of time, you are also going to kill off the sustain of the first note in a very unnatural manner. The solution is to roll the finger across the two strings by flattening it against the fretboard. This technique is not specific to the tuning you are using. All good guitarists can do this. With some practice you will be able to release the pressure on the string sounding the first note so that it stops ringing just at the point when you pick the second note. It is a bit tricky at first but once you get used to it, it is both comfortable and fast. Be aware that it is a lot harder to roll down toward a lower string than up toward a higher string. When you roll up you don't have to prepare, or know in advance what you are going to do. You play the first note normally and flatten your finger when the time comes. When you roll down, however, you have to start with your finger in the flattened position on the higher string and with a point of contact further away from the tip than usual. Try to ensure that the tip of your finger rests against the lower string when you pick the first note. If you fret the first note with the tip of your finger, as you normally do, you won't be able to reach the lower string without bending the note on the higher string.
|Fret the low string, 3rd string in the picture, with the tip of your finger as you normally do||Fret the higher string, 2nd string in the picture, with the finger flattened and the tip resting against the lower string||Video demonstration using 1st and 4th fingers (download mp4)|
Rolling obviously works only when moving across adjacent strings. If you need to move 2 or more strings away in the same fret you need to figure out a suitable fingering for it. A useful exception to this rule is that it is feasible to move several strings up by using the first finger as you would with a bar chord.
On a classical guitar the distance between adjacent strings is significantly greater than on an electric guitar so if you play a classical guitar only occasionally, as I do, you will probably find the rolling technique very difficult. In principle, I don't see any reason why it shouldn't be possible to get used to it, you just need to fret the note on the higher string even further away from the tip of your finger.
It shouldn't be necessary to practice the rolling technique on its own unless you really are the perfectionist type. You can acquire the necessary skill by going through a healthy number of examples that require you to use it. I never practiced it specifically. I learned it by going through Ted Greene's Single Note Soloing Volume 1.