Are you mad to consider more trees? YES! In 10 years the Poinciana will completely dominate that space; there'll be absolutely no room for the corymbia, which is itself enough to dominate the space. If I were you, I'd plant no more than the frangipanny and maybe the magnolia at a goodly distance from it, though in the sub-tropics it'll be a bit too warm for it to flourish at its best. Like many beginners to gardening (myself included a few years ago) you're falling for the tendency to plant too close; to over-crowd your allotted space. Be generous, take notice of the labels on the plants (which are at times over generous anyway) and plant with discipline. If I were you, one small to medium tree for shade and much lower bushes for the understory. Consider 3 levels, tall(ish), medium and small. And allow plenty of room for them to develop. Another tip: take a walk around your neighbourhood and check out the sizes of the mature specimens of the plants you mentioned.

I have to confess to being an over-planter. It's just blind enthusiasm and impatience I suppose. Your subject says it all... so many trees!
I've certainly had a couple of reality checks over the years.
What you have to consider is that the mistakes can come at a price. A considerable one financially if you are needing to remove mature trees or constantly lop ones intruding on your neighbours. Or a turn-off to potential buyers if you want to sell and your market is not so green.
That said, your choices did not seem so deadly to me... given the distances and your soil, I reckon you won't see anything absolutely taking over for well over 10 years.
The frangi can be butchered and restarted from cuttings anywhere anytime it is unsuited to its spot.
Personally I found the little corymbias quite manageable and a gem magnolia is hardly going to take over the world.
(Your ultimate problem is actually going to be that poinciana :-) but we all know who to blame for that decision).
Your under planting isn't going to be any easier for years, none of the trees will provide much shade. IYou would be better off looking at summer sun-stopping options for a few years while you get your understory plants going, even if in pots that you shift around. Shade sails might work, also large tubs of clumping bamboo that will grow quickly, even temporary arches of vines that can be sacrificed later when you have the shade you need. Bamboo, thatch products, trellises and a bit of ingenuity should give you a cooler feel for a while. Don't discount a couple of cheap water features and water plants, either - a few tubs of waterlilies or cannas plus gold-fish and a little solar pump can do quite a reasonable job on the cheap

Thank you both for your advice. A small update: I no longer have to worry about the corymbia as I rethought it and have planted it in the front yard. Yes, I agree the poniciana is going to end up being a major PIA but some people will not listen.

The idea of temporary potted shade is fabulous, allisonoz! I didn't think of it. I am definitely going to follow up your suggestions and get myself some clumping bamboo and trellis some vines. And it's funny, I've just been googling water plants this morning so obviously it's meant to be.

Thanks again for the education and inspiration.