FSK modulation in baseband
The expression $g_i(t) = e^{j2\pi f_i t}$ is not the baseband signal--- it is simply the positive frequency portion of your bandpass signal. To convert this to a baseband signal we need to take the further step of frequency translating the modulated signal centered about the carrier frequency $f_c$ to baseband $f=0$ as follows:
$$f_b = g_i(t)e^{-j 2\pi f_c t} = e^{j2\pi f_i t}e^{- j 2\pi f_c t} = e^{j2\pi (f_i-f_c)t}$$
$$= e^{j 2 \pi (f_c+\alpha_i \Delta f - f_c) t)} = e^{j2\pi \alpha_i \Delta ft}$$
This is further demonstrated with the spectral plots below showing the difference between a passband and baseband signal: