I have one of the original Kenmore HE3t washers (2003), and it has both a pressure switch and flow meter.
If you want to add more water manually, you have to wait until the machine stops filling for the wash. If you don't, you rinse levels will be off.
The way my washer works is that it measures the amount of water it adds for the wash, stopping the fill process once the water level sensor detects enough water. It doesn't use the same level for the rinse, but rather adds a percentage more for the rinse - ignoring the water level sensor during the rinse. So a large load of towels, which soak up a lot of water, have a higher rinse level than a smaller, lighter load, like dress shirts.
If you add water during the wash fill process, then the washer will "think" the load didn't absorb much water, and the rinses will have less water than they need. But if you wait until it is finished, it is not a problem. You have to add a heck of a lot of water to trip the overflow switch, cause it to drain the water and display an error.
You can add extra water to a rinse at any time, as soon as the rinse fill begins. The washer will still add its predetermined amount of water, so you will get a deeper rinse.
I noticed a bug in the software, at least in my machine. It occurs if you add extra clothing after the wash cycle finishes filling, even if the add a garment light is on. If the added items absorb a lot of water, extra water is added to the wash to compensate, but it doesn't include the extra water it added into the rinse water calculation, so the rinses will contain a shallow water level. Also, if you start a load with sopping wet clothes, then the rinse amounts will also not contain enough water.
Joe