Based on the total flux, and photometry, usually they will assume a model for the star formation history. Sometimes a single burst, a constant star formation rate, an exponentially declining star formation rate, or maybe a combination of multiple bursts. The strength of the Balmer Break and the UV slope can be good indicators but even in this case, there are large uncertainties. I haven't read the paper but this is how it's often done in general. Of course, the type of stellar populations you use, impacts from dust, and the fact that star formation histories are rather complicated can impact accuracy.

The used a series of observations across a broad spectrum I didn't read the paper, but I suspect the number of observations was quite large.