There are 3 general methods to progress towards the early arm swing used at elite levels when performing swing time ( and multiple) somersaults in routines.
The most commonly used method is now the arm set methodology.
A half and half method is to arm swing into beginners skills and learn an arms up alternative to every move depending on what sort of skill follows.
The least common methodology is to use an arm swing methodology into every move up to and including front and back somersaults, but introduce an early arm swing for swing time somersaults and beyond.
There are advantages and disadvantages to every method, but the methodology currently being taught on all coaching courses is the arm set method. This is the method we will be using from now on.
A short presentation follows to highlight the development of arms in our club members.

The reason for wanting arms up as you finish one somersault is that it increases the moment of inertia and so slows the incoming somersault. This allows the performer to fine tune their entry to the bed. Used without thinking this can obviously cause the performer to lose balance if the somersault is under rotated.
Common myths are that having arms up makes the performer go up in a straight line and reach their maximum height without travel, but used in the following way the arm set method removes the difficulty of teaching arm swings into skills.
Progressions for Bedford flyers TC coaches from 2010
For beginners teach every skill with arms above the head for the take off and the landing phases. No arm swinging to arm sets up to award 7.
At award 8 teach early arm set as a stand alone skill. As the performer progresses teach later and later arm set to reach vertical by the bottom of the bed.
Teach arms up for take-off for all moves until the skill is well performed and needs to have more height.
At that point introduce arm swing to early arm set to skill combination.
As the performer progresses, migrate all moves to leave arms down on exit to the
Shape at top and just before entry to the bed move arms up to reach vertical by the bottom of bed.

Wait until somersaults are well established and introduce either arms up on exit to the Shape or late release to arms up on entry to the bed so that they are vertical by the bottom
Then teach swing time into next somersault without mentioning arm position
Performers will not even notice the new arm position for the take off to the next somi!
Once established introduce arm sets and remove the first somersault if necessary