We are fortunate that we live in Florida where technically speaking we can grow plumerias longer than most other areas. So for new seedlings I just keep them in the covered patio where they get bright light or indirect sun but protected from frost. Or you can place them inside on a southfacing window. I never saw the need to use grow lights on my seedlings.
I don't normally let my seedlings go dormant on the first year of growth but I water them only when soil is dry during winter times. Seedlings like moist but not wet feet, they are tender so they could rot easily.
A mini-greenhouse would probably be a bettter investment in FL than grow lights?