Myth
The founders in Philadelphia changed the rules. They knew they could never get 13 states to agree to the new Constitution, so they cheated the process and said that the Constitution would go into effect as soon as 9 states had ratified.
Fact
The Philadelphia convention merely proposed a new ratification process. The convention had no real and final powers to establish the Constitution.
It would be for the states and Congress to agree or not with the convention's proposals.
Congress agreed
The convention transmitted two documents to Congress - the proposed Constitution and the Resolutions of Transmittal. The Resolutions of Transmittal contained the new ratification instructions. Congress was given no role in the new process. They were asked to simply transmit both documents to the 13 state legislatures.
Congress could have refused to transmit the documents which would have amounted to a rejection of the new ratification process. Or Congress could have transmitted them to the states, signaling approval. Congress ended up sending both documents to the states.
Congress approved of the new ratification process.
The States also agreed
The legislatures of each state also received the proposed Constitution and the Resolutions of Transmittal containing the recommendation that the each legislature establish ratifying conventions in its state. As with Congress, any state could have rejected the new ratification process by refusing to create a ratifying convention. And if any state had refused, the old ratification process requiring unanimity would still be in effect.
But every legislature (even Rhode Island) voted to create ratifying conventions in its state, signaling unanimous approval of the new ratification process.
Ratification process appropriately changed
With the new ratification process now having the unanimous approval of the states and of Congress, the Constitution could now be ratified according the new process: ratification by 9 state conventions.
The Resolutions of Transmittal
source: https://avalon.law.yale.edu/18th_century/ressub01.asp
Rhode Island Ratifying Convention
Even Rhode Island's legislature agreed to create a ratifying convention for its state.
They didn't initially approve of the Constitution but they did approve of the new ratification process.
source: https://www.loc.gov/resource/bdsdcc.c0901/?st=gallery
