If by the term "transition time" you mean the natural lifetime of the transition, then there is no link to wavelength, except for a general trend that transitions of lower wavelength tend to have shorter natural lifetime. The situation is that if the natural lifetime is $\tau$ then the transition rate $\Gamma = 1/\tau$ typically goes as
$$
\Gamma \propto |M_{ij}|^2 \omega^3
$$
where $\omega = 2\pi c/\lambda$ is the transition frequency and $M_{ij}$ is the matrix element describing the coupling between atom and electromagnetic field.
However it seemed to me that your question is also asking something else, namely how can it be that a transition that can take a long time (e.g. natural lifetime could be as long as 1 second) can nevertheless feature a photon whose arrival at a detector may be a sudden event. This touches on the general fact that a wavefunction can be spread over a range of position and time, but a suitably constructed observation of the relevant system can be concentrated in position or time.
In the case of emission of a photon, both aspects are on show. As the light propagates away from the atom, the wavefunction associated with the electromagnetic field goes in all directions, expanding outwards with spherical wavefronts and an amplitude distribution over angle which is typically a dipole emission pattern, but can be other shapes. And yet a position measurement of the photon will find it to be at one particular place.
Similar statements can be made about the timing. Once the atom has been excited, its interaction with the surrounding electromagnetic field (which may typically be in its ground state) begins immediately and the joint evolution of atom and electromagnetic field is that the atomic dipole oscillates and the field picks up an excitation in the form of a wave of many wavelengths, oscillating and decaying in amplitude. The wavefunction of the emitted photon (I am here employing a slightly rough-and-ready concept, in order to avoid the field theory details) has a form roughly given by
$$
\psi(r,\theta,\phi,t) = \frac{a(\theta,\phi)}{r}
e^{-t/2 \tau} e^{i(kr-\omega t)}
$$
For example, if the natural lifetime of the atom is 10 nanoseconds and the frequency of the light is $10^{15}$ Hz then the wave-train will last about 10 ns and will have about $10^6$ wavelengths. However, if you position a detector of electromagnetic energy, such as a photo-multiplier tube, in this wave-train, then it will register an excitation at one particular time, an excitation having the entire energy of the emitted light. That is the marvelous nature of quantum mechanics, and if you wish to look into this process more deeply, you enter into the area known as the quantum measurement problem, which tries to unpack exactly how the many-possible-times-and-places gets resolved into one-particular-time-and-place.
To pick an example to bring this out, the atomic natural lifetime could be much longer, say one second, but the detector can react much faster, say one nanosecond; in this case the detector clicks abruptly at some moment chosen randomly, with a probability distribution over time corresponding to the 1-second exponential decay time of the atom.
In the present example one speaks of "a single photon" and what I called a wave-train can be considered to be a mode of the electromagnetic field. This mode has gained a single degree of excitation; that is why there is just one photon, and why the detector clicks just once. The timescale on which the detector transitions from "no click" to "click" is set by its own internal dynamics.
If one wanted to demonstrate experimentally that the electromagnetic field mode here really is spread out in time, as I have said, then one could do it by using a temporal coherence measurement. For example, one would split the wave into two parts at a beam splitter, sending one part on a longer journey via a mirror, and then recombine, and there would be an interference effect. Of course to get convincing evidence such an experiment would have to be repeated many times.
