Arrival time of single photon cannot be mesaured presicely. The best detectors have random error order of 0.1nsec with 10..100psec statistical sigma spread.
IRF is measured using laser providing very short pulses and good time reference signal. IRF is importnat because it defines minimal width of timing spectra that be resolved since it comes as convolution into any observed TCSPC plot.
1. The IRF is a way of characterising the system itself, it tells you how the excitation beam is arriving at the computer. There are a number of factors that can influence this, see this page: https://www.edinst.com/instrument-response-function-widths-minimum-measurable-lifetimes-in-the-fls1000/ for more details of the factors that can distort the original excitation pulse.
2. Rise Components are when the measured fluorescence decay has a lifetime component with a negative A-factor. This appears as a broadening and skewing of the decay, such that the peak is no longer sharp and may be a few ns from the IRF peak. This is observed in samples with excited state proton transfer when the initially excited molecule [T1*] undergoes tautomerisation to another excited state [T2*] and emission is seen from both tautomers. See doi:10.1016/j.jphotochem.2011.10.024 and DOI: 10.1111/j.1751-1097.2012.01140.x for illustrated TCSPC decays