We present a systematic analysis of heavy-flavour production in the underlying event in connection to a leading hard process in pp collisions at s=13 TeV, using the PYTHIA 8 Monte Carlo event generator. We compare results from events selected by triggering on the leading hadron, as well as those triggered with reconstructed jets. We show that the kinematics of heavy-flavour fragmentation complicates the characterisation of the underlying event, and the usual method which uses the leading charged final-state hadron as a trigger may wash away the connection between the leading process and the heavy-flavour particle created in association with that. Events triggered with light or heavy-flavour jets, however, retain this connection and bring more direct information on the underlying heavy-flavour production process, but may also import unwanted sensitivity to gluon radiation. The methods outlined in the current work provide means to verify model calculations for light and heavy-flavour production in the jet and the underlying event in great details.
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