Ask an Economist
If I run a manufacturing company and I pay people to do work, presumably those hours are in the manufacturing sector when it comes to measuring the nations's productivity. If I also pay consultants [who's hours belong in the service sector] to help with that manufacturing volume, are those hours counted as service or as manufacturing?
The output determines which sector a particular activity falls under. If the output is a good (product), then it falls under the manufacturing sector. If the output is a service, then it falls under the service sector.
In your particular example, the output of the consulting company is a service, so it would fall under the service sector. However, that consulting service is an input in the manufacturing sector.