If you run the same or similar samples frequently, you can have a good idea at what conditions the oligo of choice elutes. Trityl groups are far more hydrophobic then the acetylated failure sequences so the reversed phase separation is driven by the synthetic method. The triethyl portion of TEAA has equilibrium with the hydrophobic surface and the positively charged amine ionically pairs with the anions. For unprotected oligos, think of TEAA and reversed phase as a type of solvent eluted anion exchange. C4 works well and will not bind reaction products as tightly as C18.
Reversed phase is a good single step for easy oligos and initial research purification.
Eluting off the acetylated failure sequences, 2. On-column base cleavage of the trityl group, 3. Removing the oligo without its hydrophobic anchor, 4. Removing the trityl group with higher solvent. Removing the trityl group from the collected oligo and re-injecting onto the reversed phase column is a two step purification.