ASR does not show much effect on Geopolymer concrete, because Geopolymer has less alkaline in nature.For example fly ash consists of 1-2 % of alkali. The percentage of alkali in fly ash depends on the thermal power plant.when1-2% this react with silica in fine and coarse aggregate in concrete it will not show much effect.
Yes, ASR is still a major concern in geopolymers due to the high alkalinity of the activators used. So far in open literature, there is no conclusive observation yet; some studies have shown high expansions in geopolymer concrete due to the high concentration of sodium hydroxide used as activator, while some other studies show that no significant expansions with the use of reactive aggregates in geopolymers.
I believe this area still need more dedicated research in order to have conclusive observations. These articles might help;
Article Impact of Alkali Silica Reaction on Fly Ash-Based Geopolymer Concrete
http://www.flyash.info/2011/155-Patil-2011.pdf
https://www.scientific.net/KEM.302-303.248
Article Alkali-Activated Binders: A Review: Part 1. Historical Backg...
Article Geopolymer Technology: The Current State of the Art
geopolymer concrete or geopolymer mortars haven’t ASR issues , because alkaline ions are inside the matrix of hardened material. There isn’t migration to surface so no alkaline carbonation occurs and durability is assured . No leaching , no too many salts in surface , no ASR. If you check pH of surface you find that is almost neutral or little bit alkaline, while if you broke the material and check internally pH you will find higher. This property is only one , but there are many others that shows differences between geopolymers and alkali activated materials. They aren‘t the same products , in geopolymer technology don’t exist any “activator“ and pH of silicates , that are named “reagents or hardeners”, used are lower and less dangerous than pH used for alkali activation.
Find more clarification on geopolymer.org , that is the only one Official source of correct information about this technology.