TL;DR
Thermostatting / barostatting in ensembles such as NVT, NPT, etc, introduces an exchange of energy between the simulated system and a virtual "bath". You should ensure that whatever you are observing in simulation is a property of the system, not of its coupling to the thermostat / barostat. For a first pass, I would recommend equilibrating the system in a relevant ensemble, then switching to NVE for the excitation and subsequent dynamics.
The Physics
It looks like you are interested in exciting some species in a simulation volume, and tracking where that energy subsequently goes. Most likely, (1) you have some species or degrees of freedom to which energy can be transferred, and (2) the excitation is with an electric field / photon. Quantum-mechanically, the absorption of a photon is fast. In a classical potentials-based molecular-dynamics simulation, a classical interaction of charged particles with a field can also be simulated - ignoring polarizability or including it with a shell model.
Most likely, absorption / excitation is the fastest process. The next slower one is the coupling of the initially excited degree of freedom (electronic / phononic / translation / rotation) to others within the system. Most likely (see "nonlinearity" in limitations), the excited degree of freedom will transfer energy to lower-energy ones, which are definitionally lower frequency and work on longer timescales. If excitations are sparse and/or localized, there will ultimately be some heat diffusion happening as well. While all of this is happening, the system has more energy than it should, and is out of equilibrium.
Here is the most important part: in simulation, the thermal coupling to "bath" is usually much faster than in experiment, because simulation is a much smaller system than in reality. Heat transfer from something like an excited molecule to the substrate on which it sits takes nanoseconds in real life, see for example Fig 7 in this paper. But we cannot tolerate a thermostat that takes so long in simulation, which means that thermostatting pulls energy from the simulation more rapidly than is really physical. It does so by coupling to higher-energy degrees of freedom in the system and slowing them down.
Practically, this means that thermostatting will affect more dynamics than is physical in a non-equilibrium simulation with excitations. The easiest solution to this is to equilibrate the system first, then simulate the non-equilibrium dynamics in NVE, and note the temperature rise. The next easiest is to simulate a range of thermostatting parameters, and only trust the results in the range where changing the thermostat does not change the observed dynamics.
Literature
There is a rigorous body of work simulating the excitations of molecular motions and vibrations in liquids. Notably, they have used both classical MD and ab initio MD. The ab initio lets them study polarizability and second-order (induced-dipole) effects. In approximate chronological order, there are a few pure simulation papers, one and two and three, and a few experiment + simulation papers: one and two and three. I am not sure what to say or highlight about these works other than they have looked at a variety of aspects of this type of simulation, and benchmarked them with experiments. A keen reader could pay attention to the analyses used to track the partitioning of energy between various degrees of freedom, and how the simulated excitation strengths correspond to the experimental ones.
Absolutely shameless plug of my own work: I've used classical MD to look at the excitation of ionic translations with light, pre-print here. I took five steps to ensure I could trust the results: (1) used a system with the fewest possible confounding degrees of freedom (2) used NVE and noted the temperature rise (3) made a very large simulation to get enough rare-event statistics (4) used an excitation field that is equal to the experimental one to minimize confounding contributions from nonlinearity (5) interpreted only the most salient, qualitative trends rather than the quantitative rates. The simulation is probably quantitatively wrong, but the trends are probably qualitatively right.
Limitations
First, this answer deals mostly with classical, nuclear-dynamics stuff. It may be possible to just put a field into an ab initio simulation and simulate electronic excitations. But I don't know for sure. If you want to do a proper electronic excitation, someone else should answer with how best to do it in ab initio, TD-DFT, etc.
Second, the excitation and dynamics of interest may be rare; beware averages. This happens most at higher frequencies / energies as quantum effect become prominent. See for example this paper about water (disclosure: I worked with some of these people), where to match the simulated effect to experiment the excitation fraction had to be taken into account. Experimental excitation strength / density may be much smaller than what is practical to simulate while still getting a simulated signal - but the dynamics at simulate-able strength may not be the same as at an experimental one. Separately, the dynamics of interest could also be a small shoulder superimposed on some larger effect you may not care about, as in my work linked above.
Third, nonlinearity happens. Nonlinearity and anharmonicity of vibrations are integral to the transfer of energy between degrees of freedom, and to heat transport in the first place. Polarizability and induced-dipole effects may happen. If electrons are involved, weird stuff like impact ionization may happen. Nonlinear processes such as phonon upconversion turn on with excitation strength. In general, I recommend being very careful about the excitation strength used in simulation as that will affect subsequent dynamics: try a few, or go as low as possible, or match an experiment.
