Warwick Bloodhunt; why doesn't it always activate?

What I mean is, Warwick's Blood Hunt activates whenever an enemy takes damage, and his new health count is 50% or below.

This means that if Warwick respawns while the enemy Makrsman is at, say, 20% health, Blood Hunt will not activate until the enemy takes damage.

Now I wonder, is that intentional? Sometimes it feels bad to respawn, try to chase your enemies out of base but the Blood Hunt never procced on them. Can certainly understand if it was intentional, but I couldn't find any information on that. Would appreciate if someone can link otherwise as necessary.