Most UV light curing adhesives cure with a free radical polymerisation process. When the correct wavelengths of UV light are absorbed by the photo-initiators in the adhesive, the photo-initiators generate chemically reactive free radicals. These induce cross-linking, or polymerisation, of the oligomers and monomers in the adhesive, resulting in a polymer of cured material.
If the surface of the adhesive is exposed to atmospheric oxygen during the cure, oxygen can penetrate the very top layer and inhibit polymerisation. This causes an incomplete surface cure, leaving unreacted oligomers and monomers ― the tacky residue. We would define tackiness as when you feel a tack as you rub your finger across the surface, and get traces of wet residue on your gloved hand. Of course, if your bond is completely interfacial and between two surfaces, then oxygen inhibition will not occur, since the adhesive is not exposed to oxygen.
In situations where the joint design has exposed adhesive fillets and a sticky surface occurs, the bulk of the adhesive is cured and what the manufacturer is detecting is a very thin layer of adhesive constituent. Structurally, the bond is likely to be quite sound. However, it can be undesirable from the perspective of contamination or aesthetics.
Modern adhesive formulations are less likely to have tacky surfaces when cured with the correct equipment, as chemists have become clever in mitigating it, so it is more likely with older products or softer adhesives. Bear in mind that some soft adhesives may be formulated with additives that remain sticky when cured and can appear to be signs of oxygen inhibition when they are deliberate properties of the cured adhesive.