Hmmm... I'm using the Apple branded one. I believe it converts TB3 to TB2 or something? Anyway, have you tried turning off any MOTU interfaces that are connected to the Mac Studio via TB *before* shutting down the Mac?
I have a MOTU 828es with a MOTU 24Ai daisy chained off the back of the 828es via Ethernet (AVB). If I power down the 828es prior to shutting down the Mac Studio, I *never* have the rebooting problem. I've reported to MOTU and they should be able to reproduce and investigate on their end.
ADDENDUM: As we all know... nothing it seems works perfectly, so remembering to shut down the 828es before shutting down my Mac is an acceptable workaround to me for now. I bought two of these:
https://www.amazon.com/gp/product/B0812 ... UTF8&psc=1
... and I installed one in each of the left and right rack bays built into my studio desk, so I can power on/off various effects our outboard gear with a switch on these units. I'm actually very happy with the build quality. Switches are sturdy... there's an LED that indicates if power is on or off. There's an "always on" outlet front and back and two USB charging ports of the front, although be forewarned... they'll charge a phone but they won't charge an iPad. Anyway... I just flip the switch for the power to the 828es on that before powering down.
As an aside, I was very happy to discover that if I hooked up my Samsung 43" 4K TV that I'm using for my main monitor to one of the outlets, I can turn the TV on of this way. I do not need to use the TV remote as I did when I just kept the TV connected to constant power. It seems like the Samsung is designed so if it's not seeing power and the plug, and then it's turned on, it turns on the TV! Great thinking by the engineers there!