It seems that Refresh and probably Revitalize don't improve with their caster's Healing EMP. The heal of refresh and probably revitalize will improve if the character affected has a star on Healing EMP. https://imgur.com/a/n2xm2
Topic on User talk:AdlaiT
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This has been known for a long time regarding refresh effects. Refresh effects are essentially self-healing effects. The same can be observed with refresh and 
Healing UpHealing skill's healing amount is boosted
effects such as from 
Yggdrasil Omega.
It's better to have a Refresh page that explains all of this rather than individually noting this on character pages.