Evolution is a timed fusion
An evolution needs two things at once. A weapon at its maximum level. Its named passive also held.
When both are true and you open a chest at the right moment, the pair fuses. The result is a single stronger weapon with new effects.
Why it changes the run
An evolved weapon outclasses two separate ones. It frees a slot and hits harder than the parts did alone.
Late stages assume you have one. Without it, the damage check at the end gets rough.
Set it up on purpose
Do not wait for the chest to appear by luck. Know which passive your target weapon needs and grab it early.
The passive items guide lists what each passive does so you can plan the pair.