No, they auto-tune during each startup/reboot. Been that way for many batches now.
This is simply not true! They run the autotune routine ONLY on first start or after a hard reset (possibly on other rare occasions), but definitely not after every restart be it clean or unclean. There is a flag set in the filesystem that triggers the autotune routine. Maybe somebody could point out where it is exactly - cannot remember off the top of my head. Source: Operating S9-13.5TH/s miner.
It seems as though you have a major misconception about what the auto-frequency is and how it works. "Autotune" is an uniformed, social-media contrived name based on too many misconceptions of what happens in the process. When it comes to "newer" models of S9s, auto-frequency has a specific frequency set for each chip. This frequency is set in the PIC, and this setting is done prior to shipping to the consumer.
I have to say I must differ a bit on that.
Yes the as-shipped info is read from the PIC and Auto-tune then runs some tests to see if the settings work. When they do, great! Pre-heat/Health checks are done in around 5min.

IF they don't - it then tries a lower frequency to see if all chips in the chain pass inspection. If the chips pass that lower freq is what it runs at until rebooted.
And yes this test is done each time you cycle the power AND do after a soft boot.
Proof? My s9 batch-18, the only 'lower-speed' one of their batches I've bought. Is 11.2THs as I recall.
Yes, it runs at spec'd speed but a) board-1 runs a bit more than 150MHz slower than the other 2 boards. b) more to the point, it can take 3-4 soft boots to get it to that speed. The 2x lets call then 'Prime" boards always report same speed and within a couple 10's of GHs of each other every time. The weak sister: speed will vary more than 75MHz from it's usual of 425.5, sometime higher (for a while but also has high HW errors, yes is a long timed run) more often it boots at lower speed but zero HW errors after even 1 hr. Keep kicking it until I see 425.5MHz when tuning is done and I know it will be fine until the next boot(s).
The Kernel logs report it all...