I did INTL-INTL connection at BOM few months ago. Interestingly it was to CX (BOM-HKG) 0130 departure.
I arrived well in time from EU and the receving agent said he'd help and asked me to wait in the transit area. This area, not surprisingly, is well staffed by AI and indeed seem to be moving the AI traffic along, well. After about 30min. wait and my escort nowhere in sight, I proceeded through immigration/ customs, hence arrived in India. Went up to the departure level and checked-in with CX, just in nick of time. I may have been the last passenger to have done so. Flying in Business class helps too.
Caution: have a print out of the CX reservation handy. You may need it go through departure security.