No problem there with oscillations. In my career, I had worked on autopilots for manned and unmanned air vehicles, where the problems you described would be bad, very very bad (control system theory was my graduate topic too). On this sous vide setup, there is no problem mainly because the thermal mass is high, and the heat source is limited (230W on Hi as I measured). Once, I saw the temperature continuing to rise up to 136F after the controller had switched off, but that was it.
So, how was the experiment?
A qualified failure! Let me explain further.
I "cooked" the steak for 3 hours, as it was still cold. I had some Montreal seasoning, so rubbed the steak with that. After 3 hours, when I pulled the bag out, I saw that there was something like 1/2 cup of juice in the bag. I did not expect that much. Did the bag have a pinhole? No.
So, I seared the steak, then deglazed the pan. Not a whole lot of flavor there as I expected, because the meat did not stay long to release much juice, nor that I wanted it to. So, along with a bit of butter, I poured the meat juice into the pan and reduced it. Then, seeing that the sauce was still thin, I reinforced it with some half-n-half as I did not have some creme on hand. A bit of garlic and several grinds of fresh pepper and dinner was served. Meanwhile my wife made salad and sauteed some asparagus.
The meat was nicely cooked and pink throughout as expected. No meat juice ran off as I cut it, unlike the usual steak. But as I cut, I saw that this steak was not tender. And upon chewing, aye aye aye...
I told my wife that it was such a bad steak, and I could not remember having one so bad. Perhaps 30 years ago, when I tended to overgrill them? Yikes! It was a bad cut of sirloin, that my wife bought from a supermarket that should remain nameless. This must have come off a cow that was a great-great-grandmother. Aye, aye, aye... My wife said her half was OK, and gave me some. Quite better, but still subpar. Man, I told my wife we should just get steak from Costco, which tended to be more reliable. The piece we had would make a good stew, not steak.
So, instead of melt-in-your-mouth steak like Springnr had, I got a stick-between-your-teeth steak! I am going to compensate by pouring myself a shot of Cognac now. Gah!
By the way, here's the photo of the controller. No photo of the steak as I was too excited to taste it. Poor me!