The 31-day figure you were given is plausible and here is why it matters legally.
Interstate detainers operate under specific rules governing how long one state can hold someone on behalf of another. Under the Interstate Agreement on Detainers and related state laws, the requesting state has a limited window to come and take custody of the person once they are being held. If Virginia placed a detainer and the local jurisdiction is holding him on Virginia's behalf, Virginia has to act within a defined period or the hold can be released.
The specific timeframe varies depending on the states involved and the nature of the underlying violation, but 30 to 31 days is a commonly cited window in many jurisdictions for an out-of-state detainer on a probation violation. If Virginia does not send a transport officer or otherwise exercise its authority to take custody within that window, the local facility may be legally required to release him rather than continue holding him indefinitely on another state's behalf.
Whether that release actually happens on day 31 depends on how strictly the local facility follows that timeline and whether Virginia makes any move to extend or act on the detainer before the deadline. Some jurisdictions release automatically when the window expires. Others give the requesting state additional time if requested.
The most direct way to get a reliable answer is to have an attorney contact both the local facility and Virginia's probation authority to find out exactly what Virginia intends to do and what the binding deadline is. That information determines whether the 31-day release is real or just an estimate.