They had no paid ministers and therefore no salaries to pay.

They were from the very beginning entirely self-supporting, and the missionary could, and did, leave them and go to others who needed him more.

But in this case there was no mission compound, no elaborate system of mission education, and no mission fund from which the chapel could be built and a pastor provided, before the converts were ready to provide these things for themselves.
Most commonly the mission does all these things, and then self-support does not necessarily imply independence of foreign support.

We have met native Christians who assured us in one breath that they were members of a self-supporting Church and that their Church did not receive its fair share of mission funds.

Self-support does not necessarily mean independence of external pecuniary aid.
What then does the status of a self-supporting Church imply?
Nothing certain, but just what the society, or the missionary, chooses.