to do and is usually only seen when someone starts at higher body fat levels and is completely new to weight training.
They are also typically eating a lot more than 1300 calories.
You will absolutely get leaner and stronger and smaller from weight lifting while at a calorie deficit focused on fat loss. Sounds like you went about it the right way for that kind of goal.
But to add 15 lbs of actual muscle at that restricted amount of calories like he claimed is not physically possible.
It's also MUCH more efficient to focus on one goal at a time.