The orbit separated proton cyclotron (OSC) described in [1] differs in concept from that of a separated orbit cyclotron (SOC) [2]. Synchronous acceleration in an OSC is based on harmonic number jumps and orbit length adjustments via reverse bending. Four-turn acceleration in the OSC enables it to have four times fewer cryogenic-cavity systems than in a superconducting linac of the same high beam power and energy range.Initial OSC studies identified a progressive distortion of the spiral beam orbits by the off-axis, transverse deflecting fields in its accelerating cavities. Compensation of the effects of these fields involves the repeated use of a cavity field map, in a 3-D linac tracking code, to determine the modified arc bends required for the OSC ring. Subsequent tracking studies confirm the compensation scheme and show low emittance growth in acceleration.