Blumhouse is a brand/IP hybrid. The studio's films almost all share strong thematic, aesthetic, and tonal similarities. You can fairly consistently determine that a film is from Blumhouse from watching the trailer in a way you absolutely cannot determine, say, a Columbia or Paramount film from its trailer. It's very much akin to golden age Hollywood, when studios tended to have a strong house style - in fact, Blumhouse films tend to vary a lot less then those classic studio products. Comparable modern parallels would be the output of Marvel Studios or, to a lesser extent, the horror output of A24. Insidious absolutely does not stand apart from this - in fact, it is very arguably the most standard example of the Blumhouse "house style."
That "house style" is becoming oppressively boring at HHN.
If Five Nights was going into the Coconut Club, the sign would say "Five Nights at Freddys," not "Blumhouse." They would trumpet it. Five Nights isn't going to be at the event, and its no loss.