I don't have a copy of AMS5524 available to me.  But many production specs of alloys (for instance just calling out AISI 316, or the equivalent UNS number, or certain ASTM specs) specify only the chemical analysis limits and not heat treatment condition.  Type 316 is available in various conditions and strength levels from cold work.  If someone specifies annealed then usually it means solution annealed for which there are cooling time/temperature limits to guarantee the part is not sensitized, which reduces corrosion resistance.  If solution annealed the strength will be at the lowest available in the alloy as all cold work will have been removed.  If the material has been heated or cold rolled then it no longer counts as annealed, unless the final step is a solution anneal. 

I hope that this is helpful information.  It is usually best to have a copy of the relevant year revision of the referenced specification which can be purchased online from SAE or other sources for less than the cost of an hour of engineering time.