Based on my knowledge of the antibiotic doxycycline and its basic pharmacodynamics, it doesn't appear to be a contradiction. Upregulation is the term for a persistent increase in a cell or bodily pathway's homeostasis conditions for a given substance. For example, doxycycline could upregulate the protein NF-κB by increasing the number of protein receptors on the cellular membrane that conform to the protein shape.
Inhibition refers to a reduction in the proportion of a chemical's pharmacological activation. For example, doxycycline could inhibit the protein NF-κB by decreasing the sensitivity of the cell's protein receptors. This could happen at the same time as an increase in the quantity of those protein receptors. Since the two terms do not describe inverse phenomena, they are not a contradiction.