I tried this too and had a bit of a different experience in Terminal 3.
Firstly the transfer desk is marked as Garuda Indonesia, so if there are no Garuda flights landing then no one is at the transfer desk. I was trying to do an international to international transfer (i.e. a quick turn) but landed late at night so no luck there.
I asked some airport employees who mostly said that I had to go through immigration.
I then asked the immigration officer, who said I needed to ask another guy, who said I need to ask the help desk. The help desk said that I need to ask the transfer desk, but if no one is at the transfer desk, you can just go upstairs.

To make the picture clear: when you arrive at CGK T3, you are in a big hallway with all of the other arrivals. On the right you will first see the visa on arrival desk (and ATMs), which currently costs 500k IDR + a processing fee of 13,500 IDR. Next, you will see a green arrow which marks the transfer desk. Directly after this (and before the duty free shop) there will be an escalator going up (which says security and gates) which is not blocked off. After this, there is a duty free shop then the actual immigration (e-gates and counters and help desk).

At the top of the escalator there is a small security checkpoint. They checked the documents and verified that I was flying on the same airline (wasn’t GA). That seemed acceptable so we proceeded with the security screening and then I went through back into the T3 departures area. If you are on two different airlines, it might be a bit trickier, no guarantees if the desk isn’t open.