Granular mixtures segregate radially by size when tumbled in a partially filled horizontal drum on short timescales. The smaller component moves towards the axis of rotation and forms a buried core, which then forms undulations that grow into axial bands. Experimental and simulational studies have provided differing accounts of the type of transport taking place in radially segregated and self-diffusing grains. We investigate the bulk axial transport of small quantities of tracer particles travelling amongst glass spheres using non-invasive high-speed synchrotron x-ray particle tracking, which allows us to access timescales not explored previously. The mixtures used have varying propensity to axially segregate based on the glass sphere sizes when the tracers are present in larger proportions; we found that the single-particle dynamics of these mixtures when the tracer concentration is low do not appreciably depend on the relative particle sizes, implying that the potential for a mixture to axially segregate cannot be inferred from the microscopic dynamics of individual small particles. From the single-particle dynamics, we also found that while the standard measure of diffusive behaviour, the slope of the mean-squared displacement, is close to that expected from diffusive transport, more detailed analyses indicate anomalous transport.