Calorie deficit = no muscle mass gain. so why am I stronger?

Okay, my arms have always been very skinny- my husband calls them spaghetti arms.
There was barely any fat for muscles to hide under.
I eat at a deficit but see definite muscle definition in my arms and shoulders that I didn't have before.
So, how does that fit into your explanation?

1.) Your muscles fill with water/glycogen as a result of strength training, making them look more "full". This is not true muscle tissue gain, even though the muscles do appear more prominent.

2.) Even though you may not have had much fat covering the muscles, there was still fat there. As you lose it, muscle definition increases, revealing the fuller/more prominent muscles from 1) above.

How long do your muscles stay "full" after strength training?
Is this temporary only lasting a few hours etc. or permanent if you continue to lift on a regular basis?

1. noob gains (some muscle growth is possible in a deficit initally, but this stops after a short time)
2. increased blood flow within the muscles combined with increased storage of glycogen (and therefore water) within the muscle causes an increase in size that's often mistaken for muscle growth. this is known as "pump" in bodybuilding terms, and is frequently mistaken for muscle growth. Again, the muscle will not get bigger indefinitely from this, and in fact the pump goes away if you don't continue to work out regularly. This is the reason why a lot of women stop strength training, thinking that they put muscle on really, really easily and will turn into the incredible hulk if they continue. You can see a pump sometimes even after just a few workouts. I saw this in my shoulders and upper arms after just 1 week of stronglifts, but I knew it wasn't real muscle growth, just "pump"
3. after a pump and noob gains, you won't see your muscles get visibly bigger while eating at a deficit. Real growth of actual muscle tissue is really difficult to achieve, it requires a lot of training and eating at a surplus, and a lot of patience because it's slow for men to grow muscles, and even slower for women.

QFT. As a chick who has intentionally bulked twice over the last 2 years... I can attest to this. Building muscle is HARD. I have spent many months eating at a surplus and training like a beast to gain just a little more mass. In fact, I suspect it's going to take me at least 2 more years (bulking 7+ months each) to get to where I want to be in terms of muscle mass. I was eating upwards of 3000 calories per day towards the end of my last bulk. If my surplus only yielded me small-to-moderate mass gains then I assure you... you can't be making much progress in a deficit!

...and here are a couple great articles by Lyle McDonald addressing muscle mass gain (and why it isn't happening in a caloric deficit):

http://www.bodyrecomposition.com/muscle-gain/general-philosophies-of-muscle-mass-gain.html

http://www.bodyrecomposition.com/muscle-gain/muscle-gain-mistakes.html

^^^ this. there are some special circumstances where you can gain a little muscle at a deficit, e.g. noob gains, muscle memory gains (e.g. where you regain muscle that you recently lost)

Also, gain in lean body mass does not mean growth of muscle tissue. Gain in lean body mass could be all kinds of things, including your muscles storing more glycogen which results in water weight gain, other water weight gains (e.g. from eating too much sodium), it could be a gain in bone density, there could be more food in your intestines, etc..... lean body mass is the weight of all of your body that isn't fat, and so a gain in lean body mass does not necessarily mean you've actually gained new muscle tissue.

As for strength - a lot of strength gains come from neuromuscular adaptation, i.e. your muscles get better at responding to the exercise and using more of the muscle fibres that you actually have, and using them more efficiently. You can see huge strength gains if you train right, without growing any new muscle tissue. After a certain level though, your body will need to build more muscle tissue to see further strength gains. but you'd be surprised how strong you can get with the muscles that you already have.

Okay, my arms have always been very skinny- my husband calls them spaghetti arms.
There was barely any fat for muscles to hide under.
I eat at a deficit but see definite muscle definition in my arms and shoulders that I didn't have before.
So, how does that fit into your explanation?

How long do your muscles stay "full" after strength training?
Is this temporary only lasting a few hours etc. or permanent if you continue to lift on a regular basis?

Permanent if you continue. It's what gives the muscle that "hard" feel when you touch it.

I am 1.5 weeks into a cutting phase (Granted I'm taking a fat burner and am supplementing with BCAAs for the first time ever). I am tracking everything.

Beginning - 178 lbs, 13.1% BF.
This morning - 177lbs, 12.4% BF.

These numbers are from calipers, read by the same person, at the same time of day.
Doing the math, that is 1.4 lbs of fat loss and .4 lb of lean mass gain. Even taking any kind of variance into account, there was some muscle gain.

I am 1.5 weeks into a cutting phase (Granted I'm taking a fat burner and am supplementing with BCAAs for the first time ever). I am tracking everything.

Beginning - 178 lbs, 13.1% BF.
This morning - 177lbs, 12.4% BF.

These numbers are from calipers, read by the same person, at the same time of day.
Doing the math, that is 1.4 lbs of fat loss and .4 lb of lean mass gain. Even taking any kind of variance into account, there was some muscle gain.

As a personal trainer, I'd think you would know that the inherent error/variance in skinfold caliper measurements is generally accepted to be in the 5% - 15% range. Accurately measuring a 0.7% change in BF% is a pretty dubious reach.