Heres a picture

Here's the root buds

Not sure what the shrub is - purple leafed plum, maybe? - but what you've really done, it seems, is force the cuttings into bloom as many people do with forsythia and other shrubs for winter/early spring color. It is unusual to have had this occur after three months, but it is not the same thing as rooting cuttings.

There are many good online sources which explain in detail how to root various types of shrubs, but in general it involves wounding the cutting, treating it with rooting hormone, placing it in a mixture of peat and perlite, for example, and enclosing it in a poly tent to maintain high humidity. The treated end of the cutting first calluses over, then produces roots. The rooting compound goes on the wounded part of the cutting, not in water or in the soil, to help in this process.

It is possible that the second photo shows incipient roots, as some very easy to root plants like willow, will put out roots in water. The trouble with this practice is that the transition from water to soil is difficult and can result in the death of the roots.

In your particular case, the cuttings have no roots so they will have no way to absorb nutrients or water if you move them into potting soil. Since they seem to be in good condition, it may be worthwhile to try rooting them using the method outlined above. Move them now, though, and they will not survive.

Thanks.