Apparently one means of detecting WIMPs is to search for a photon ejected when one interacts with matter. If we don't know its mass or velocity and the weak interaction implies the absence of charge, why is a photon released?
The central idea is to detect the recoil of a nucleus caused by the interaction with a WIMP. That recoil can then have various physical effects which can be detected. In a scintillating material, that effect would be the emission of light. But it could be the apparition of bubbles in other type of detectors using a superheated vapour called… bubble chambers! There is also a setup using crystal at very low temperature where the recoil would induce detectable vibrations. So your question becomes two-fold: (1) what is a scintillating material? (2) How does the WIMP make the nucleus recoil. For the former, I'll leave you with the Wikipedia article. For the latter, the exact interaction between the WIMP and the nucleus is very model-dependent (there is an enormous zoology of Dark Matter models, to mention just that), so much so that experimentalists don't go into these details usually. They just assume the scattering is elastic, which is enough to compute the recoil of the nucleus for a given mass of the WIMP. Then they use astrophysical models to guess the distribution of Dark Matter in the vicinity of the Earth, predict an event rate, and then scale their detector accordingly. After collecting data from some time, they can go in reverse and estimate an upper bound on the density of WIMP.
You do not give a link for your assertion:
Apparently one means of detecting WIMPs is to search for a photon ejected when one interacts with matter
In this paper for example:
Indirect Detection of Dark Matter with gamma rays
Indirect detection searches for the products of WIMP annihilation or decay. This is generally done through observations of gamma-ray photons or cosmic rays. Instruments such as the Fermi-LAT, H.E.S.S., MAGIC and VERITAS, combined with the future Cherenkov Telescope Array (CTA) will provide important and complementary constraints to other search techniques
It is obvious that the gamma rays will come from WIMP annihilations or decays, and it will be part of the research project to decide what type of weakly interacting particle and which theories can be constrained using the data.
We predict the shape and normalization of the component of the flux due to final state radiation by charged particles produced in WIMP annihilation events.
There are many ways of getting high energy photons. May be there is a WIMP-->gamma gamma, for example, similar to the Higgs decay except for a long living WIMP. It all depends on the model.