How to update timezone data?
Yeah, it seems that /system/usr/share/zoneinfo/zoneinfo.* files is tzdata in java format. I tried to use TimeZone Fixer - it replaced all those 3 files. After rebooting device and enable clock synchronization via GPS on system menu, I get right time. Messaging apps now show right time too.

So, using "TimeZone Fixer" app is likely solves my issue - but app description says it could cause unable-to-boot state for some Android versions.