By 1900 the united states had created an overseas empire. was this empire a natural culmination of its expansion at home?

Yes--it was an expansion of Manifest Destiny.
No--it went beyond cultural expansion to include exploitation and control over new lands. 

In 1893, Frederick Jackson Turner claimed the days of expansion were over for Americans. This claim along with a push to gain an empire lead to expanding to islands in the Pacific and Caribbean. If the US was expanding to spread democracy and culture then the US was continuing earlier expansion ideals. If the US was looking to build a modern empire and be a colonial holder, then the ideals had shifted. There are historic arguments on both sides.