Procedures vary, depending on the jurisdiction. In some regions a time outbound will always be specified** if a DME is not included in the approach. In others, such as the USA's FAA controlled regions, IFR procedures require the pilot to stay within a certain distance (10nm in the USA) when they fly the approach but don't mandate a specific time. In this case it's the pilot's job to determine an appropriate timing outbound.
**Generally the specified time is not fixed. It's expected to be adjusted for known or estimated headwind or tailwind effects.