The flow rate on that video changes several times during the wash fill when ATC switches between mixed hot+cold (stronger flow) and reduced flow of either only hot or only cold. There's no way to know for sure which way it's shifting ... hot to increase the temperature or cold to reduce it. The ATC sensor does not measure the water temperature in the tub. The sensor is in a module located in the hose between the valve assembly and the spray flume. The flow gets too high above or too low below the target temperature for x period of time, it changes between mixed hot+cold, hot-only, or cold-only according to what it needs to cool down or warm up the sensor for x period of time so as to attain an average reading around the target. I don't see the flow rate change at any time during the rinse fill, which appears to the stronger hot+cold flow rate. I am assuming that hot+cold at that person's house satisfies the ATC warm *rinse* but is a bit too low for warm *wash* and the wash fill is switching occasionally to full hot.
There may be others but the only ATC system I've seen that directly controls the valves and mixes the incoming spray to the specific target temperature are some Fisher & Paykel models that can directly control the flow of the valves, presumably by moderating the (DC) power to the solenoids. I have one that, for example, targets 46°C (116°F) for warm. I have a tankless water heater. The water spraying from the fill flume stays at the target temperature if I set it to at least 116°F or raise it progressively to 140°F.