In my experience, just one or two washes with 1M NaOH, one water wash. Drying/concentrate... ready for chromatography.

Reaction mixture was quenched with saturated sodium thiosulphate solution. The product was extracted with DCM or Chloroform. The organic layer was washed with saturated sodium bicarbonate solution and brine solution. After drying organic layer over anhydrous sodium sulphate, the solvent was evaporated under reduced pressure and purified by flash column chromatography

The reduced product of DMP after oxidation is IBA. It is insoluble in common organic solvents. Just do a simple filtration to remove it. If you use excess DMP, add few ml of water. It will hydrolyse DMP to insoluble IBX. Filter the precipitated IBA and IBX, using any common organic solvents, depending on the solubility of your product (DCM, chloroform, acetone, EtOAc, no alcohol). Then, perform column purification for the filtrate. The filtrate may have acetic acid residue, which can be removed under vacuums or bicarbonate treatment.