What are pump probe measurements?
From the Encyclopedia of Laser Physics and Technology:


  Pump–probe measurements can be used to obtain information on ultrafast
  phenomena. The general principle is the following. A sample (e.g. a
  SESAM) is hit by some pump pulse, which generates some kind of
  excitation (or other modification) in the sample. After an adjustable
  time delay (controlled with an optical delay line), a probe pulse hits
  the sample, and its transmission or reflection is measured. By
  monitoring the probe signal as a function of the time delay, it is
  possible to obtain information on the decay of the generated
  excitation, or on other processes initiated by the pump pulses.


From the Wikipedia article on Time-resolved spectroscopy:


  Transient-absorption spectroscopy is an extension of absorption
  spectroscopy. Here, the absorbance at a particular wavelength or range
  of wavelengths of a sample is measured as a function of time after
  excitation by a flash of light. In a typical experiment, both the
  light for excitation ('pump') and the light for measuring the
  absorbance ('probe') are generated by a pulsed laser.


The "sample" is anything that you want to get the spectrogram of.

This article mentions photochemistry as one possible application. It also notes that:


  in some applications such as spectroscopy and pump-probe experiments,
  the laser wavelength must be tuned continuously during the experiment
  or test.


So, it's not that pump-probe measurements are useful when dealing with tunable lasers, its that tunable lasers are useful when dealing with pump-probe measurements.