Yes it does. Any travel in/from/to your country of residence will use an inbound/outbound day.

If you don't want to use an inbound/outbound day, then you need to buy a ticket until the border tariff point. From Aachen to Aachen Süd Grenze is quite cheap, certainly with the regional train. You then have to enter the train from the border manually, starting from Aachen Süd Grenze (in Belgium, to prevent using an inbound/outbound day).