The problem explode when you trim branches's tips. If the chaos is already there, a few complete (complete with untrimmed tips) branches must be selected and the mass of new branchlets removed. Those few selected branches will make the skeleton of the new tidy climber (for Tecoma and the others are more climbers than shrubs in the ordinay sense). Those existing tips in thse braches you have selected will keep the rest of the plant controlled and tidy. When you remove them all secondary and new branches race to be the winner. Of course, no winners and a terrible mess to deal with.
When your bignonia becomes too large for the spot and needs a reduction in size you can
a) choose a few mature branches that are appreciably shorter than the main ones. Keep these WITH THEIR TIPS and remove the main ones to the base or to the main trunk
or
b) choose a few main branches and remove the others to the base. Now cut back these branches at the selected lenght and to a secondary branchlet that will play the role of leading tip. Of course the tip of this secondary branch must not be trimed.
Hope this is clear enough (
)