Cool, this helps. Sounds like the Weather Widget may have had an issue. Could be that the widget draws on timezone data from an invalid or slightly off time source. That part of Southeast Asia has some quirks for timezone and there are a few countries or states within the countries there that are 1/2 hour to 1 hour off of the adjoining neighbors.
Middle East Time Zone Map -Worldatlas.com is one view.
Another neat way to see this is with this interactive map
Time Zone Map Hover over Thimphu and you'll see its 0630 Thursday, Nov 29. Lhasa is 0830, and Kathmandu is 0615 for the same day.
This is all probably making sense given you were in that general area, but may help to illustrate that some apps may not be designed for the mini regional time zone variances that occur within locations that are relatively close to each other as the crow flies

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The other possibility exists that your phone's clock may not have had Thimpu as a reference time source. I poked around on mine (using default clock) and couldn't find Thimphu. Kathmandu was about the closest. I then checked on an iDevice and in the Settings/General/Date & Time searched for Thimphu and its there. So if your ipod touch was configured for Set Automatically, then its possible it picked up a local time source. Since its an iPod Touch and not an iPhone, I'm not sure how it would have gotten a telecom carrier provided time source.
Back to my Android phone, I followed the same path and unchecked the Automatic time zone option, which then allowed me to select a time zone. I do not see Thimphu listed. Kathmandu at UTC/GMT +5:45 hours would have probably been your closest match.
So, the above is probably why your Android phone's time was off assuming that it couldnt get a time update from a local telecom carrier. This may also explain why your Weather Widget was off on the time. Not clear how accurate the various Weather apps are in general, or yours in this instance, are for places like Thimphu.