This is not correct for subjects. Depending on the subject level the overlord can ask for more resources than normal trade partners which the puppet then lacks in production:Resources in Hoi4 work a little different than one might intuitively assume. All Countries have a fixed part of their resources (between 80% and 0%) available for trade with other nations, depending on their respective Trade Law. Those resources can not be used in production by the owning country, no matter if they are bought by someone or not. At the same time you can never trade for the part of a countries' resources it has available for production. Meaning you could never 'drain' your puppets of resources.
On the contrary it is better for your puppets if you trade in their resources, as they get the factories you use to pay for the resources they could not use anyways.
For reference: https://hoi4.paradoxwikis.com/Trade
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To answer the original question, you will steal resources from your puppet's production lines and there is no way to prevent it. On the other hand, the subjects who are forced to give you the most resources this way usually also have to hand over most of their MIC to you as well (e.g. 65% for Reichskommissariats).