Perusing the entry for τιμάω in Liddell–Scott, the negative meaning you mention is not Epic, and first turns up in Plato and Aristophanes; LSJ describes it as an “Attic law term”. The transition is:
- to honour (since Homer)
- to award (as an honour) (in Tragedy)
- to award a penalty to someone, including a fine or a death sentence (in Attic legal contexts)
- (medial) to estimate the extent of one one’s own penalty (in Attic legal contexts)
It is a specialist meaning, and I’d expect that the main meaning, ‘to be honoured’, continued to be dominant; it certainly is the meaning you would expect in a non-legal context.