In my case, T actually packed on lean body mass while it was also burning off fat. On that note, not all of the lean body mass gains will be from muscle. Some of it will also be from ligaments and tendons thickening, as well as bone mineral density increasing. And hell, T does change your water retention a bit (I sure have noticed I go more often and for less) and so some of that weight gain will also be water weight. So in the end, it won't really seem like you've lost fat going off of what a scale alone says, but you really have.
I was the exact same weight I am now, but my mass composition is drastically different (and it was by 3 months). I basically displaced the same weight in fat that I gained in lean body mass, around 20-25lbs. I have not gained any excess fat to date (I once binged on a large Costco pizza and didn't gain an ounce), but my fat has certainly redistributed a bit (mostly from the hips and backside to the stomach).
And since without this information it would be largely considered anecdotal, more than half of my shirts are now too mall (shoulders, arms and especially in the collars) and all of my pants are now too large (slip off even with a belt unless I cinch it up real tight; suspenders are my buddies now in deference to spending $20 a pop on pants lol).
All of which happened from T alone. I was not exercising or dieting.
Ultimately, if you're not eating too much or else inappropriately (and doubly applicable if you're also exercising regularly), you should gain lean mass while losing fat at the same time on T, initially. Otherwise, you will instead most likely gain lean body mass while also gaining more fat. And which will actually be worse than if you were only gaining the muscle and not the fat at the same time and vice versa (both simultaneously make you look twice as fat than you really are).
So for me, I don't need to drop 60-80lbs anymore as I would have pre-T, I only need to get rid of 40-60lbs post-T. I honestly cannot have an excess of 60lbs of fat now. I maybe have 35lbs on my stomach, if that, to go (my extremities are normal; it's my trunk that has all the damn pudge. Hypercortisolism and hyperinsulinism are a ***** to deal with in the aftermath, let me tell you. Under-skin fat is a hell of a lot harder to get rid of than under-muscle fat). I'll never look right in the trunk without surgery to correct that marred mess. I literally look like I was clawed to shreds by a beast, so I'll still have horrendous scarring everywhere, nevermind the scalpel lines. Argh. Just praying my pelt will conceal most of that. Not holding my breath however. Ah well, could be worse I suppose).