Hi,
I use Hauppauge HD PVR and I have now .TS recording format configured. I use JRiver for almost 2 years, since v18. Currently latest 19.0.125. I have always different problems with tv recording (incl. random recorded jtv folders are not visible to JRiver).
Anyway, when I select "record current hour" and press enter to confirm and after a while I press stop, then nothing is saved. :/
I just tested it. It works.
Record current timeshift seems to "work" fine, I mean timeshift folder isn't deleted although is not converted from jtv folder to .ts file.
Have you set your recording option to TS format? If so, this is what should have happened after you chose "Record Current Hour":
Recording in TS format would start from the moment you chose the option. Recording would end (regardless whether you pressed Stop button - which would stop showing the program, but recording would go on) at the end of the current hour. The part of the program you had been watch before you started recording would be lost.
Recording does not convert current time-shifting session if you use TS recording format. It starts writing .ts file when recording is started.
On the other hand, if your recording option is jtv format, then you would get the portion of the program that you have been watching, up to the beginning of the current hour.
I also so much wish for instant recording. Now if I want to record interesting minute of news or advertisement or anything else then I have to save all the timeshift. It's waste much of disk space and make editing much harder, particularly over network. 
Two ways of doing instant recording:
1. Use a remote control, just press the "Record" button on the remote control. Recording will start instantly. Press it again when you want to stop.
2. Use OSD. Press up or down arrow key on keyboard or remote control until you see "Recording", then use left or right arrow to start recording.
