The controller outputs a signal called HOST_IRQ. At reset HOST_IRQ starts HIGH, then software will set it LOW to indicate it is BUSY and then will pull it HIGH when it is ready to accept commands.
Auto-initialization at power-up refers to the process of the Boot ROM reading the controller firmware from the flash device and transferring it to IRAM. Then the ARM processor begins to execute the MainApp that was read from Flash. Auto-initialization is complete once the MainApp has been executed to an extent for command handling from the Application Processor. If a valid Flash device and MainApp are not found in the Flash, the BootRom will assert HOST_IRQ high so that I2C or USB commands can be sent to program or reprogram the Flash.
The controller initialization typically completes (HOST_IRQ goes high) within 500ms of RESETZ being asserted high. However, this time may vary depending on the software version and the contents of the user configurable auto initialization batch file that is executed by the controller at power-up.