The reason they aren't at exactly the 1km mark is that it is based on the recorded data. Most devices record 1 data point per second. Unless your speed is constant and evenly divides into 1000m, you likely won't end up with a data point at exactly the 1km (or multiples of it) mark. 

In hardware it isn't really possible to fix without a high sampling rate, which would likely reduce battery life and may still not exactly line up with a 1km split still, especially for higher speed activities where the distance between each point is larger.

In software you can make an estimate based on the average speed over that split, but it probably won't be perfect. Alternatively you can pull the full data stream (using https://developers.strava.com/docs/reference/#api-Streams-getActivityStreams) and calculate the splits yourself, again estimating/interpolating the intermediate distances. You'd get a better estimate since you would have the speed at each data point.