Please see Bemidbar 16:27. Why is Korach’s dwelling called a Mishkan rather than an ohel or bayis?
You are bringing up an interesting point. A possible answer may be the following. The Chizkuni (Shemos 38-21) on the words “Eyleh pikudei Hamishkan, Mishkan Haedus” asks, why does it say “Mishkan- Mishkan Haedus”? In order that we shouldn’t mix up the MIshkan with any other Mishkan- for example the Mishkan of Korach. According to what he says, it could be that Moshe meant to hint to Klal Yisroel should distance themselves from the idea that Korach wants to make his own Mishkan, i.e. in a different way then H-shem set it up, that Aharon is the Kohen etc. See Sukkas Dovid on that verse.