Frangipani (Plumeria) are tropical plants from the Americas, but have been naturalised to other parts of the world - especially Asia and the Pacific.
So it looks like they need warm weather.
As a tree / shrub, it sounds like outside would be ideal. GardeningTipsAndIdeas suggest they should be okay in the lower third of the US. So they must have some frost tolerance.
References are Australian but the SacredGardenFrangipanis.com website has much more useful information, including this snippet:
How to care for your new Frangipani
Upon receiving your plants, they
should be potted up and kept in semi
shade or full sun in mornings and
shade from midday and afternoon until
roots can be seen coming out of bottom
The ideal potting mix, is 40%
commercial potting mix and 60%
inorganic material such as course sand
or perlite or gravel. Commercial
potting mixes are generally full of
fungus and bacteria which can be
harmful to plants.
Always water plants/potting mix with a
systemic fungicide and bactericide
when potting up your plants.