We present a detailed study of star formation occurring in bound star-forming clouds under the influence of internal ionizing feedback from massive stars across a spectrum of cloud properties. We infer which objects are triggered by comparing our feedback simulations with control simulations in which no feedback was present. We find that feedback always results in a lower star formation efficiency and usually but not always results in a larger number of stars or clusters. Cluster mass functions are not strongly affected by feedback, but stellar mass functions are biased towards lower masses. Ionization also affects the geometrical distribution of stars in ways that are robust against projection effects, but may make the stellar associations more or less subclustered depending on the background cloud environment. We observe a prominent pillar in one simulation which is the remains of an accretion flow feeding the central ionizing cluster of its host cloud and suggest that this may be a general formation mechanism for pillars such as those observed in M16. We find that the association of stars with structures in the gas such as shells or pillars is a good but by no means foolproof indication that those stars have been triggered and we conclude overall that it is very difficult to deduce which objects have been induced to form and which formed spontaneously simply from observing the system at a single time.