Why would you assume the scale is consistent? Is your water weight always the same? Do your muscles always have the same glycogen content? Do you use the scale at the same time of day every single time and did you consume the exact same diet each time, as well as take in the exact same type and amount of liquids? If not, then there is no reason to believe the scale is consistent. The technology required to scan your body and determine what is fat and what is not costs thousands of dollars and is not something you are going to find at your gym. Get some calipers and learn to do a 3 site measure so you at least have something semi-reliable to work with before you even start worrying about what ratio of your weight gain is fat.
As I stated, unless you have a serious medical issue or a hormone problem, gaining ANY weight at all will NEVER result in no fat free mass gain. Your body has to put on some lean mass in order to support any fat you have gained. Remember, fat free mass doesn't just mean muscle. It means anything that isn't fat. There is no magical form of fat that does not require anything from your body in order to exist.
Why are you cutting calories back on non-workout days? Growth occurs after the workout, not before. Unless you are lifting first thing in the morning on workout days, you need to increase the calories on non-workout days. If you must cycle calories, cycle them around the workout, not the day. So eat more the 24 hours after lifting, then for 24 hours before the next workout, trim them back.
Also, don't make the mistake of being paralyzed in fear of any fat gain. Fear leads to the darkside and all that, which in this case the darkside means being small and weak.