It doesn't really have precedent though, because Thawne was killed/negated the instant Eddie died. Past Thawne survived due to being outside the timestream, ie, he was time traveling already, so time didn't catch up to him. That part already didn't make any sense, but the rule was at least clear: destroy your past self and you die, unless you're actively time traveling, in which case you're protected. Hunter killed his past self in his own time without any out of timeline shenanigans going on. He should be dead, plain and simple. Unless there's some big reveal about his story having been a lie somehow.