Imagine this hypothetical situation (which is meant to simplify the scenario in this question):
There haven't been any past lives -- this is your first life, and therefore there is no past karma, but only the karma[s] you make in this life.
(So, in this imagined version of events, we can use the knowledge at hand without complications clouding our judgement.)
The universe is in it's first cycle, and birth has happened for the first time.
(This further eliminates any doubts of the unknown, and allows us to work with our hypothesis.)
Now imagine the following two events/actions:
Imagine walking out into the streets and seeing a hungry puppy and feeding it your lunch out of kindness/empathy and happily walking into your workplace in the bliss of doing something nice with your lunch, instead of eating it like always.
In the lunch time an old enemy of yours taunt you and this leads to a fight which ends with him arm being broken by you (intentional).
The question is: can you explain why both event 1 and event 2 would effect the next life?
As there is no Soul/Person/being in our teaching, what we have is a self responding, self generating and a replicating consciousness. If there was a soul or a being, we can justify this by saying "I am being rewarded for my good and being punished for my faults".
But we are without such permanent identities: what we have is a consciousness that gives birth to thoughts and disappears ... one thought would arise from another, but all thoughts have their own identity, apart from its parent thought (this is much like we and our parents).
On what basis can we attach the karmas of different actions together, when there is only emptiness (Anatta) between 2 different actions?