Tambo del Inka does have its own train station. However, not every train going back and forth MP stops there. In fact, very few do. They are scheduled for a daytrip with outbound in morning and return in evening.

From the hotel website :

Private Resort Train
Hours:Hours of operation
About:Onsite;
Travelers on their way to Machu Picchu delight in the direct train service offered by Tambo del Inka's private train station.

Railcar Train 601 leaves the hotel at 7am, arriving at Aguas Calientes (Machu Picchu) at 10:06am.
Vistadome Train 304 departs Aguas Calientes at 3:20pm and arrives at the hotel at 6:45pm.
Tickets are available for advance purchase at the station. Please contact the hotel at [email protected] for further details.