Do your players assume everything that dies in one hit is an illusion? To the player, what is the difference between rolling 1d6+3 for damage, getting 5, and killing a 1 HP minion kobold or a 4 HP normal kobold? Is a level 1 player-controlled wizard who rolls poorly and gets 1 HP an illusion?
Our group hasn't seen a reduction in immersion through the use of minions. In our last campaign they allowed us to simulate the rank and file troops of a street gang while the lieutenants and other high ranking figures were standard or elite enemies, with the "don" so to speak being a boss-level npc. Plus, what you suggested is exactly what the DMG suggests about encounter building; using elite and standard enemies as the more important figures and include minions as flavor.