The 135 world has played loose with the regulation for a long time. Unless you're free of all duty and have no responsibility to act for the company, then you're not at rest. It's possible to be off duty, but not at rest. Rest must be free of all duty and determined in advance.
Some (many) 135 operators will try to tell you that because you didn't fly for the past 10 hours, you were at rest. That does not meet any legal standard. Rest cannot be determined retroactively, and the FAA has been very clear on this for many years. Rest must be determined prospectively; the same principles apply to 121 as 135.
The creative applications of duty an rest policies under 135 are usually driven by budget; operators want half the pilots, and want to work them twice as much, or have them on call around the clock.
Better operators will have enough crews to have a duty period half way around the clock, so that you know you'll be called only between noon and midnight, for example, and your duty begins at noon. You know when you're off, you know when you're on, and there's no question of which is which. Many operators don't do that, though good ones do.
Duty need not be designated in advance; there's no legal requirement to do so. Rest, however, must be, and when you're in rest, the company cannot impose any legal burden for you to perform duty for the company. What is required, insofar as duty goes, is the ability to look back and find the required rest in the previous 24 hour period. That rest must have been designated in advance, and whether one goes on duty or not, once rest has ended, the look-back clock is ticking.