"I MUST connect a pull-up resistor to the open-drain /RST pin of the ADM1232. But the data sheet did not tell me to do so"

The last paragraph on p5 of the datasheet says:

"RESET AND RESET OUTPUTS
While RESET is capable of sourcing and sinking current, RESET is an open drain MOSFET which sinks current only. Therefore, it is necessary to pull this output high." (my emphasis)

The very fact that it is described as "open drain" should tell you that a pull-up is required; but even so, it specifically states "it is necessary to pull this output high."
How can you say, "But the data sheet did not tell me to do so????!!!!"