This gets interesting. Could we have a bit of confusion here, with the tipple actually serving to the King Mine, but the station being Detroit?
I looked at the ICC valuation map sheet (Thanks, CRRM!) showing Detroit, Colorado a bit beyond MP 495. I estimated it at MP 495.1. The map shows a 180 foot spur located on the east side of the main track, connected at the east (south) end, length 180 feet. According to an annotation on the map, this spur was retired on AFE T-817, in 1946. Alamosa Division Time Table 121 (Effective June 11, 1939) does not list Detroit on the main time table, Sub-Division 12-B, p. 4. However, the list of tracks not shown as stations on the time table, p. 7 lists Detroit as a three car capacity spur, connected at the east end, at MP 495.1.
This might explain why many people (self included) have believed the tipple to have been the Detroit Mine for many years. The railroad apparently called the spur "Detroit," so it seems logical for people to think that the mine it served must have been the Detroit mine, especially since it was nearby.