With regard to the Aura, it doesn't really say anything. There is no way to know for sure whether it is exactly Kaioken. However, I personally don't think it is the same for the following reasons
- In the conversation which you even posted, Whis stated that "Goku was powering up from his reserves for a temporary power boost". This seems more like Goku and Vegeta powering up in Episode 122 to fight Jiren(Goku at the start and Vegeta before the Final Flash). Kaioken is a power multiplier. Goku would be doubling or multiplying his power X times.
- Tien and Krillin are obviously aware of Kaioken and would have recognized Goku using the transformation. Tien asked Whis whether it was the same principle which would imply it was something else which seemed similar.
- Jiren compares Goku's powering up to Kale who was constantly powering up in his Legendary Super Saiyan form. The Kaioken is completely different from the same.
However, Goku's comment on it wrecking his body and Krillin's comment might also lead one to believe that Goku was possibly using Kaioken. However, since Kaioken would be a specific figure(Doubles, Triples, Increased his Power 20 times etc), and no mention of the same makes me believe it was just Goku just drawing out more power in his Super Saiyan Blue form.