Enjoy it! Looks very healthy. Lush green foliage suggests good nitrogen content in soil.

Some add phosphorus to stimulate blooming.

How many hours of sun is it getting? Too much shade may curtail blooming.

It's nothing within your control. Rhododendron roseum elegans doesn't normally Fall bloom, but when it does its likely due entirely to weather, and you can't do anything about the weather.

I have three plants with a scattering of flowers right now, I don't know what they are, were here when I bought the house but a dwarf red and two with lilac blooms, not overly showy. I suspect Spring flowering on these will be diminished, although not all buds are opening.

In soil of the right PH, rhododendrons are not particularly heavy feeders. The color of yours looks good and I think you can assume acidic soil.

It's not really that unusual for young newly planted rhododendrons to not bloom well their first year or two in the ground. But again, your Fall bloom is likely a weather related phenomenon, not something that can be manipulated outdoors.

Partial fall blooming of rhodos is not that unusual. It can be caused by warm protracted spells in Sept, especially after cooler weather. Heavy watering in Sept can promote it. Generally, the fall blooming buds never open all their flowers and the remaining ones, in that flower bud, will die over winter as they are no longer protected. As much of the east and central states had a "somewhat cool" (relatively) summer, then a heat wave in late Aug into Sept...that was unfortunately a good set up for fall bloom .

As others said , there isn't much you can do. Up here in Maine fall bloom usually isn't a problem, but Purple Gem and Ramapo, (they do well here), can often partially fall bloom. The common and not too great Cunninghams White will often partially fall bloom.

Phosphorus won't stimulate bloom.

phosphorous is sometimes used to promote setting of flower buds...whether it can promote fall bloom im not sure,