Two accepted methods of 'desalting' a protein and/or changing the buffer are dialysis and gel-filtration. Dialysis is time-consuming, and gel-filtration usually requires a concentrated sample (It is difficult to gel-filter a 250 ml sample unless a very large column is available, for example, but dialysis of such a volume is relatively easy).
You do not say whether you are using cation- or anion-exchange chromatography, but note that the charge on the buffering species is positive with Tris, but negative for phosphate, and it is usually desirable that the charge is the same as that of the ion-exchange column, as you do not want the buffering species to be exchanging and possibly exposing your protein to 'local' extremes of pH, especially if your protein is sensitive to pH changes: use a positively charged buffer for anion-exchangers such as DEAE-cellulose, but a negatively-charged buffer for cation-exchangers such as CM-cellulose. (This is the 'strategy' adopted in Chromatofocussing, and I'll bet that is why the protocol requires a change in buffer as well as pH).
Note also that a protein that binds to an anion-exhanger at pH 8 may not bind at pH 7: in Chromatofocussing on an anion-exchange column, for example, we lower the pH to elute the protein.
Ref: Protein Purification. Theory and Practice, R.K. Scopes