If you are wondering about 'tension,' no need to worry. I think CX is now letting its crew stay in CMB. (When the situation gets tense, CX usually has their crew turn around with no overnight stay.)

SQ has since 1 Jan. been offering a fast track immigration card to premium cabin pax. I would ask if CX would have a similar card.

If your brief visit means a turnaround, then just go upstairs to the transfer counter after arriving and being shuttled on a bus to the immigration area.