I can't open your capx, but I guess you could check the following things.
on start of layout set the speed of the player to 0 and check if the analog stick is in the middle of the circle.
You could also choose to put everything to do with the analog stick inside a deacitvated group and only activate it on the first circle touched.
The jump is probably set for everytime the stick goes into the upper part of your analog stick. You should try to adjust the area affecting the jump. Maybe even create extra sprites within the circle which on overlap will trigger the jump.
I haven't been able to open the capx, but I've seen the analog stick-example before, If my answers don't make sense for your implementation I hereby apologize.