In Quartus,
Tools -> IP Catalog
In IP Catalog,
Library -> Basic Functions -> Configuration and Programming -> Remote Update Intel FPGA IP
https://www.intel.com/content/dam/www/programmable/us/en/pdfs/literature/ug/ug_altremote.pdf
This is used to reset the watchdog timer function built-in and starting reconfiguration based upon parameters you set during user mode with this IP. As far as selecting between various images this IP would be required. Depending upon how one wishes to reconfigure flash this IP might not be needed. One could erase flash and overwrite the flash at base address zero without any backup, but this carries the risk of not being able to recover from a poorly written flash or power cycle during the writing. Plus, you still need a way to start the reconfiguration process which if a simple power cycle is sufficient that could be done.
There are a few flash controllers, so I am not sure the one being referred to at all. I believe various could be used to achieve a similar result. I will say it is possible to set-up a Quartus project to use the active serial pins such as dclk, cs, data0, etc. as user I/O (this is under the Dual-Purpose Pins" section). Meaning one can make their own flash controller if a custom interface is needed or you already have something designed.