Learn Finnish: Pelastettuaan minut sankari ei saanut kokemuspisteitä. - After rescuing me, the hero did not get experience points.

This is the past temporal construction, which translates to "after doing". You build it by taking the passive past participle (pelastettu), adding the partitive ending (-a), and finally attaching a possessive suffix (-an). Even though the base building block is a passive participle, the possessive suffix gives the construction an active meaning: "after he rescued".

How do we know who did the rescuing just by looking at pelastettuaan?

The possessive suffix -an tells us that the action was performed by the subject of the main clause, which is sankari. If the rescuer had been someone else, you would state the doer in the genitive case and drop the possessive suffix entirely. For example: Poliisin pelastettua minut... (After the police rescued me...).

Why is the object of the rescue minut instead of the partitive minua?

The temporal construction takes an object just like a normal verb clause. Because the rescue was a successfully completed action, it requires a total object (accusative case). For personal pronouns like minä, this specific accusative form ends in -t (minut).

Why is the second object, kokemuspisteitä, in the partitive case?

It is the object of the main clause, which is negative (ei saanut). In Finnish, negative actions almost always force the object into the partitive case. Here, it is in the partitive plural because "experience points" is a plural concept.