Just FYI, when you are recording in TS format, and also have Time Shifting turned on, both files formats are written in parallel. There is no conversion between the two, or demuxing from TS to JTV format. The stream is written twice, once to each format. Time Shifting is always saved in JTV format, regardless of the recording format selected.
I am not positive (because I'm just a user like you), but I think that if you are recording in TS format, and use Time Shifting to move back and forth in the program, then MC would be playing the JTV files, not the TS file.
If you watch a channel live without recording, and then try to Time Shift within the program, you should be able to find temporary Time Shift JTV file in your TV recording folder, should you go looking. Normally those are deleted once the Time Shift session is ended.
So it sounds like both your Time Shifting issue, and problems with recording in JTV format, are related to the JTV format used. Your observations make sense to me, based on the above information: JTV recording isn't working properly.