Hi Sweet Sailing and welcome.
I am sure every place is different. You will likely end up emailing or phoning a marina where you plan to stay and reprovision. You can glean local knowledge at that time. We often do Singapore-Malaysia-Singapore.
Leaving
Singapore we file our immigration plan 2 days in advance and the crew is "pre-cleared" our boats port clearance is also completed with the crew manifest - We then sail out to the quarantine
mooring and while protocol says you fly a Q flag and hail immigration & customs on VHF we only hail. Immigration comes by
boat and we drop our documents in a basket. 5 minutes later they pass back all the passports and a signed & stamped copy of the port clearance. Our club does the paperwork for us for US20 but you can do it yourself.
Malaysia has 2-3
ports of entry near us. We sail directly to a port of entrance, tie up and proceed to immigration & customs. They stamp all the passports and issue a port clearance. No pre notice is required for
Malaysia. Then we are free to sail to our
destination.
Upon leaving we visit a port of entry and the passports are stamped. Returning to
Singapore we proceed directly to the Q zone and hail immigration on VHF. Immigration comes anywhere from 20-45 minutes later, stamps the passports and we proceed home. No pre-clearance required coming back. Technically Singapore does not allow you to go ashore without visiting immigration.
Indonesia is more complicated and a "cruising book" is required for the
boat. This is like a boat log and must be prearranged in advance.
Indonesia is a bit more of a hassle to be honest.
The exact phrasing (to your original question) for Singapore goes something like:
"Singapore Immigration this is sailing vessel Relax Lah!, Relax Lah!, Relax Lah! on VHF 72" (repeated twice)
"Vessel calling Singapore imigration, say again" - (Ha, ha)
"Singapore Immigration this is sailing vessel Relax Lah! on VHF 72. We are at the Eastern Quarantine and request inbound/outbound immigration clearance"
"Relax Lah! Stand by"
From then on they show up or you call back. If it is busy you can hear them working other boats and often you can see them. You wait your turn...