Just to make sure I understand - you're putting the meter in VAC mode and shorting the leads?
My limited testing shows that my "higher end" meters (87V, BM786) tend to take about 10 - 12 seconds to drop down to something around a 1mV reading, and they don't ever get to zero (or at least it takes more seconds that I was willing to wait around for - which wasn't anywhere close to 1+ minutes). Though this isn't universal - my BM235 drops to zero within a few seconds.
My cheaper, no name meters tend to immediately drop to zero.
If you look at the specs for VAC, I think you'll see something about readings having much less accuracy at below 10% of the range. For example, the 87V manual says, "Below 10 % of range, add 12 counts". 12 counts in the 600.0mV range of the VAC mode is 1.2mV - and that's on top of the 4 counts specified for the range in general.
The specs for the BM786's 600.00mV range simply say, "Accuracy specified from 10% to 100% of range". In other words below 60mV all bets are off. The specs for the UT61E say the same thing.
I suspect that you are right that the TrueRMS functionality has something to do with it, but I honestly don't know. Note that your UT61B isn't True RMS.
I'm pretty sure there was a thread about this behavior in the last several months, but I couldn't find it.
I was about to say that your UT61E is in good company, but then I realized that your meter starts out at several volts - mine start out at something less than 100mV, including a UT61E I have on hand. It takes my UT61E almost 10 seconds to drop to 5mV when I short the leads. How long does it take yours?
I'm not sure whether or not having an open circuit reading that high is an indicator of anything.