I have never 'water'rooted' anything. I may be in the minority. But I just don't see the point. I think it is a personal preference, but I think it can carry a risk of things rotting. Especially if the cuts to propagate were made with tools that were not cleaned properly. If I want something to GROW in water, I toss it in there--no container--- and let it do its thing (this works well for a surprising variety of plants...hoya, epiphyllum, syngonium, spathiphyllum, alocasia, colocasia, chinese evergreeen, costus ginger....I could post several more that I have found out by accident will grow as hydrophytes.
When a rootless plant (or in your case a plant with the beginning of one root) needs to re-establish itself, rooting in water can work. It requires VERY BRIGHT LIGHT. But the roots a plant produces in response to water rooting are different in their ability to function to support the plant than the roots they would develop in soil. They are thinner, more fragile, and do not uptake nutrients in the same way. When a plant with water roots is placed into soil, these roots function more poorly at the outset than would roots that established themselves in soil in the first place. They have to then develop a whole new set of soil roots. In the meantime, growth can stall, and the plant can drop leaves or look sickly when the plant takes energy from them to try to do this. Then people get freaked out and think their plant is dying. And it may.
There is a proper way to transfer a water root plant to a soil root plant, however, but to me, its a time consumer and I do not have time to mess with such. You take your soil and basically make it into mud and place the water roots in that and gradually 'dry the soil out' over a period of time until the plant has had time to redevelop the root structure it needs to make it in the ground.
I have just never seen the need for this. Captan is a good product to stop rot, it i a wettable powder that can be made into a slurry. When I get new barefoot rhizomes for plants like the Zingiberales from the mail, I soak them in a little Catpan slurry before I pot them up. I don;t do this with plants I get as trades locally because we always leave the plants in pots and just dig a hole and plant them directly. But anything that has been cut, dig and cleaned, had roots removed, I treat to have a better chance against the establishing plant rotting as it red-roots. It is also commonly used to prevent damping off in seedlings of many plants at time of transplant. A slurry of a tiny amount of captan in water brushed onto an orchid leaf that has black spot will stop it. Using it on the end of a broken leaf on an orchid will stop the brow die back and further leaf damage.
I am not a professional. I am just an older lady who has been growing a wide variety of tropical plants since about 1983. I propagate my own variegated monsteras and various anthuria and philodendrons on a regular basis for myself, in order to increase the number that I have growing, and all I do is cut a shoot off and stick it in a container of my tropicals mix. Works well. When I deem it large enough I plant it next the the support I want it to start climbing.