I have a Tipu (brizilian rosewood ) tree and the spittle bugs are very annoiing. Please some advise will help.
The spittlebug nymph is encased in a foamy covering so it's hard to control with a contact insecticide. A systemic insecticide that is applied a soil drench for root uptake is appropriate for non-food plants like your ornamental tipu tree.
I don't know what insecticide products are available in South Africa, but look for an active ingredient of acephate or dinotefuran. These are both very fast acting systemics. Be sure to water adequately before and after the soil treatment to facilitate uptake. Examples:
https://www.domyown.com/bonide-systemic-insect-control-p-1533.html
https://www.domyown.com/safari-20sg-systemic-insecticide-with-dinotefuran-p-2512.html
See other considerations and option is this article:
https://www.gardeningknowhow.com/plant-problems/pests/insects/spittlebug-control.htm
I am concerned about this because I know that tipus have invasive root systems. The tree was dug up with its root ball and planted elsewhere but I assume the gardener could have missed some of the roots.
That is true of most trees. Just watch the area for any regrowth and treat it with a stump killer if it returns. Here is more about the tree:
https://www.gardeningknowhow.com/ornamental/trees/tipu-tree/how-to-grow-tipuana-trees.htm
https://www.gardeningknowhow.com/ornamental/trees/tgen/kill-zombie-tree-stump.htm