Take a look at the original sentence again:
My cat Buster is always tipping over the garbage
can then he searches through the trash for
milk jug caps, which he bats around the floor, the cat version of playing
ice hockey.
You chose to fix it the correct way:
My cat Buster is always tipping over the garbage
can, and then he searches through the trash
for milk jug caps, which he bats around the floor, the cat version of playing
ice hockey.
My cat Buster is always tipping over the garbage can is a main clause. Then he searches through the trash for milk jug caps is the second main clause. A comma and a coordinating conjunction like and is a great way to connect the two main clauses that create the fused sentence.