If the emissive state/species and the state you're probing with transient absorption are the same state you should get the same lifetime from a TA decay trace and time resolved emission. That being said, unless you have a chemical reason/evidence why you should be seeing multiexponential decay you need to go above and beyond to prove the sample is pure and the multiexponential decay isn't due to sample impurities.

Thanks Catherine E Mccusker