Gaining fat would indicate that you are taking in a surplus of calories which isn't such a bad thing. Some of what appears to be fat will be water which is more transient. You may have gained fat all over rather than just on the gut, but just notice it there. You could monitor if you are getting fatter by purchasing a skinfold caliper.
You don't have to work out your bodyfat with it, just keep an eye on the measurements. Coupled with your scale and mirror you can get an idea how much you are gaining is actually muscle.
As far as training for strength goes what are your goals ? Following the program you are on would increase strength and mass.