We study ionization of atoms in strong orthogonal two-color (OTC) laser fields numerically and analytically. The calculated photoelectron momentum distribution shows two typical structures: a rectangular-like one and a shoulder-like one, the positions of which depend on the laser parameters. Using a strong-field model which allows us to quantitatively evaluate the Coulomb effect, we show that these two structures arise from attosecond response of electron inside an atom to light in OTC-induced photoemission. Some simple mappings between the locations of these structures and response time are derived. Through these mappings, we are able to establish a two-color attosecond chronoscope for timing electron emission, which is essential for OTC-based precise manipulation.