No they don't wobble, I've used them on two T5s and a T6 (one T5 I had was fitted with factory swivels). They run on nylon rollers and when in the forward facing position have safety fitments to secure them in position in the event of collision.
I currently have one over a leisure battery under a driver's seat.
The only downside is the poor handbrake lowering kit supplied for the driver's seat box. The best solution for this is to move (or have moved) the existing hand brake bracket down and slightly forward. Like all T5/T6 driver's seat swivels the hand brake has to be off to rotate the seat, this even applies factory fitted swivels.