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Woody plants (trees, shrubs, and woody vines) don't often root in water when a cutting is taken for propagation. Usually, they need to be dipped (cut end only) in rooting hormone gel or powder and put under a high-humidity or frequently-watered setting, in a pot with potting soil, in order to root. The rooting process can take several months, and not all woody plants root as readily from different types of cuttings. In general, there are three types of wood used for cuttings: softwood (tender growth that's still fairly floppy and doesn't have any stem bark yet; the stem is easy to bend without breaking); hardwood (older growth that has stiff wood and bark on the stem; the stem will snap if bent); and semi-hardwood, a stage in between those two phases.

The blooms didn't appear on the cutting on their own; flower buds are present on Rhododendron and Azalea branches months before they open in spring. The cutting is merely acting like a cut flower stem at the moment, and just like cut flowers whose buds aren't open yet can open them later, the same has happened here. Rooting hormone that is diluted in a jar of water will not be concentrated enough to work, unless that's how the product label directs it to be used (we're not familiar with any that work this way).

We don't expect that any Rhododendron or Azalea cutting will root in water. The cutting may be too old at this point, but you can try taking it out, re-applying the rooting hormone to the cut end of the stem only, and putting it into a pot. It'll either need frequent attention if put outside (as a container may dry out often as it warms up; put it in shade so it doesn't get sunburned) or put under bright lights and a humidity-retaining cover if kept inside until it roots. It's possible it will never root, however, if it was taken at the wrong growth stage or the tissue has gotten too old from being cut for so long.

Nurseries that propagate these plants put cuttings under a mist bench (a table in a shaded greenhouse that runs sprinklers for short periods of time over the cuttings multiple times a day), and it takes many weeks or longer for them to root. The trick is to have the cuttings never dry out (since they can't use roots to absorb water yet, and their leaves are gradually losing moisture) yet not stay so soggy that the stem rots or other fungal problems develop.

Every reference we checked for tips on propagating azaleas from cuttings has slightly different procedures. You can explore several other Extension web pages that have information about propagating azaleas from cuttings. The Azalea Society of America also has propagation tips on their website (see the linked page) that might be helpful.

Miri

You're welcome!