I have gotten lipstick foam, riding Forward Seat. Not all the time, by any means, and not on all horses.
As to WHY I get foam riding Forward Seat, well I try to have a “conversation” between the horse’s tongue and my fingers. To have this “conversation” the horse’s tongue has to move the bit. Enough of this and some of the horses I ride produce the lipstick foam. I have NEVER, in over 45 years of riding gotten ropes of saliva dripping from the horse’s mouth, but then, when I even bother to use a nose band, I make sure I can get two or more vertical fingers between the nose band and the horse’s lower jaw bones.
When I get these “conversations” going with the horse my riding teacher always exclaims on how the horse’s jaw, neck and top line visibly relax. My seat feels the horse’s back "swinging. To me these “conversations” with the horse’s relaxed tongue are one of the supreme joys of riding. The horse’s jaw is relaxed, the tongue is relaxed and “playing” with the bit, the poll and neck relax, and the horse and I swing along with lightness, joy and happiness.
YMMV. I do not ride dressage, and with my MS my hands are not always as stable as they could be. Even so the horses are usually willing to “converse” with me through the bit and reins.