Each beast has its own morphology and MO, but there may be parallels with the three species of Acarapis suggesting that Tropilaelaps could feed on adults.  The two external Acarapis presumably feed through intersegmental membranes in the notum and wing axillaries.  The tracheal one somehow gets nourishment through the walls of the prothoracic trachea.  A single female after entering the trachea deposits a sequence of very large eggs (about one a day), starting from close to the spiracle and going further into the trachea.  They are obviously full of fluid and burst easily, so some access to the haemolymph by the laying female is the most likely explanation.  The nymphs emerging from the eggs are also almost as large as adults and likely have to feed to complete their development.  They likely also access haemolymph through the walls of the trachea. 

An early effort to produce artificial feeding scenarios for mites:

https://hal.science/hal-00890952/document

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