Blood Spatter Analysis is sacrificed for having five or more bloodstain counters on it only while its second ability is resolving. If you put a fifth counter on it some other way, it won't be immediately sacrificed.

You don't choose a target creature card to return from your graveyard to your hand at the time Blood Spatter Analysis's second ability triggers. Rather, a second "reflexive" ability triggers when you sacrifice Blood Spatter Analysis this way. You choose a target for that ability as it goes on the stack. Each player may respond to this triggered ability as normal.

Blood Spatter Analysis's reflexive triggered ability triggers and returns a creature card to your hand only if you sacrifice it while resolving its second ability. It won't trigger if you sacrifice it for any other reason.