My understanding is, even when the speed is less than 13 and in full battery, engine will restart when the air conditioner units, temperature falls below the expected value. When it can no longer provide cold air using the frozen substance[1], it will restart the engine. This is clearly mentioned in the below quote from their site[1]
Wagon R's ISG only provides assistance to the engine when accelerating for few seconds and for starting up of the engine. So when you take you foot off the brake, engine has to start, since at the beginning, it doesn't run with the mortar(ISG). ISG only engages when you are accelerating and the engine power is not enough to provide the required acceleration. Please read the bellow quote from their site
[1]. http://www.globalsuzuki.com/corporate/environmental/green_technology/#ecoCool
[2]. http://www.globalsuzuki.com/corporate/environmental/green_technology/#idling