Trumpet vines bloom when roots are well established, the plant has good vitality, and woody tissues achieve a certain genetically predetermined (ontological) age. When you cut the plant back, you reset the ontogenetic clock because new tissues are younger. Confused?

From an old post I left on this forum:
"To a certain degree, the flowering of all (perhaps I should hedge and say nearly all) plants is dependant on tissues reaching a certain ontogenetic age before tissue differentiation into flower structures is possible. Ontogenetic aging is roughly a measure of the number of cell divisions that must occur before flowering. It varies from plant to plant. An illustration of its influence can be seen in the fact that plants propagated from cuttings invariably flower/fruit sooner than plants of the same species from seed. The tissues in the cuttings have seen many cell divisions and are ontogenetically older than tissues from seed, thus they are capable of flowering sooner. It is interesting to note that cuttings taken from basal portions of a plant are more vigorous because they are ontogenetically younger than cuttings from top branch tips. However, the cuttings from the ontogenetically older wood at the upper parts of the plant will flower sooner."

If you wish to read the entire post, I'll leave a link to it, below.

Dividing trumpet vine would be like dividing a woody shrub or tree - not usually propagated that way. Clone from cuttings or basal offsets as they occur. As the plant matures, you will be blessed with hundreds, even thousands of opportunities for new plants as root-sprouts are likely to occur in profusion in the near vicinity of where it's sited. It can be a very invasive weed.

Al

Here is a link that might be useful: More info if interested