We performed femtosecond reflection spectroscopy on a series of perovskite-type cobalt oxide $R$BaCo$_2$O$_{6-delta}$ ($R$=Sm, Gd, and Tb) crystals, in which the electronic transfer was controlled by $R$. The transient reflectivity and the optical conductivity ($sigma^{rm PI}(omega)$) obtained by Kramers-Kronig analysis showed an ultrafast change within a time resolution ($approx 150$ fs) at room temperature and the appearance of signals of a hidden state different from the high temperature metallic state. The transferred spectral weight in $sigma^{rm PI}(omega)$ upon photoexcitation sensitively depended on the $R$-species, indicating an important role of electronic correlation in the photoexcited state.