Though you would think that Thiazides would only worsen the effect of Diabetes insipidus by increasing urine volume, it has the unique effect of upregulating sodium reabsorption in the proximal portions of the nephron.
So you can think of it this way. In the distal part of the nephron, you are blocking NaCl reabsorption at the connecting tubule and thus NaCl end up in the urine, increasing the osmolarity
Salt loss -> ECF volume contraction -> Upregulated sodium reabsorption proximally and water follows. This is a petty attempt at getting as much water back in as possible. The literature doesn't have a clear explanation on this as it doesn't seem to be mediated by RAAS activation.
Source: Loffing, J. Paradoxical Antidiuretic effect of Thiazides in Diabetes Insipidus: Another Piece in the Puzzle. JASN 2004;15:11pp.2948-2950