While some pilots may believe they must be within a specified distance of a fix or geographic point, such a condition, while helpful in maintaining situational awareness, is not necessarily required.
The following references suggest that the aircraft must be on the centerline of the subject course, and at the assigned or prescribed altitude.

According to the FAA Instrument Procedures Handbook, FAA-H-8083-16B, Chapter 4:
For aircraft operating on unpublished routes, an altitude is assigned to maintain until the aircraft is established on a segment of a published route or IAP. (Example: “Maintain 2,000 until established on the final approach course outbound, cleared VOR/DME runway 12.”) The FAA definition of established on course requires the aircraft to be established on the route centerline. Generally, the controller assigns an altitude compatible with glideslope/ glidepath intercept prior to being cleared for the approach.

From the AIM:
When operating on an unpublished route or while being radar vectored, the pilot, when an approach clearance is received, must, in addition to complying with the minimum altitudes for IFR operations (14 CFR Section 91.177), maintain the last assigned altitude unless a different altitude is assigned by ATC, or until the aircraft is established on a segment of a published route or IAP. After the aircraft is so established, published altitudes apply to descent within each succeeding route or approach segment unless a different altitude is assigned by ATC.