The answer is “it depends.”
Generally installing a JHF on a gateway requires a reboot (usually not on management).
When you’re doing a version upgrade on the gateway (going from say R80.30 to R80.40), that most definitely requires a policy install afterwords.
If the JHF has content that impacts policy compilation (obviously on management), which changing gateway version does, then you may need to reinstall policy for the relevant changes to take effect.
However, I would expect the need for this to be documented in the JHF notes.