“Normally” (as in installed with MyOSMC and/or the Howto on this forum) tvheadend resides on the same device as osmc?! Or do you have a seperate machine for that? But as I said, I did not do that much further reading on this, so to find out if, from whom and where the caching happens, you would have to dig into some help files or a search engine of your liking.
But: If your system is plugged into a CEC-enabled device (most recent TVs with HDMI), you could try to disable and enable video playback on CEC-events (i.e. powering the TV on/off) and see if that helps: [HowTo] for auto quit/start kodi based on TV status - #9 by dbarciela
EDIT: Another read on this: CEC adapter options