Puffiness is a common response to beginning a weight-training program. Extra fluid around muscle fibers is a part of the repair process. This should go away after a month, though.

Whole-body puffiness, on the other hand, usually means you're retaining water. Are you getting enough salt?

Also, you didn't mention if your lifts had increased. Are you seeing improvements in strength?

Since you said you keep a caloric deficit, my only real question is have you been lean pretty much all your life? If you're running/cardio lean and never did much weight lifting, just give your body time to start getting use to it all. I know when I went from biking miles upon miles to mostly weight lifting, I started to look truly fat. After a few weeks of weight lifting and having to increase weight, I started getting definition.

Give yourself some time, see if you get noticeable changes. Also if you go from cardio to weight lifting, look at getting more protein if you don't get enough, and perhaps try to increase food intake a bit rather then staying too much in a deficit.

A lot of people opt to deal with looking puffy until they put on the desired amount of muscle they were striving for. During that time they eat what's necessary to most efficiently gain a lot of muscle which may or may not correlate with remaining 'cut' looking. Then afterwards they go on a specialized diet that maintains muscle mass but cuts fat.

I suggest this way ^ or else you're going to be battling yourself for a long time. It's a shorter route to gain fat & muscle and then lean yourself out afterwards.

Why calorie defect if you're already lean to begin with? These new workouts you added come at a cost. In the form of extra calories(energy from food for you holistic hackers who don't believe in calories). You can cause a cascade of hormonal health problems while exercising on low cal.

There are to many possibility of why you look puffy. From my gym experience guys get puffy because

1. Water retention. Possibly from creatine in your case if you're paleo diet consist of extra red meat (beef,lamb,venison,buffalo. I'm getting hungry as I type this)
2. To much fat & carbs. Too much energy here can lead to fat & muscle gain. Bulk/dirty bulk
3. Training in general pumps the working muscles with extra blood. That's why you'll look rip/bigger after a workout.

All the above is what I am thinking...Plus, the role of cortisol. Any stress, physical or emotional, will raise your cortisol level. Cortisol plays a very large role in water retention/secretion (about 50% I believe). If water rention is what is causing your puffiness, this could be your contributing factor. Looking at your schedule, you are not giving your body too much time for rest and recovery and it will catch up with you. Remember, cortisol can be catabolic. In a calorie deficit, trying to put muscle on will be a more arduous task for your body = more stress (cortisol). You may find it beneficial to to a refeed now and again, timed with workout days. (You can look up the Minessota experiment for case studies on this). A note to your last comment - you CAN actually get and maintain that lean/cut look while adding muscle. It's about timing and properr training. Treating your body like a yo-yo like most builders do will cause more damage than good. Remember, muscles don't grow in the gym (or wherever you are working out). The rest/recovery is just as, and possibly more so important. You may also want to check out Leangains...Hope this helps!

Might need more details on your routine and progress. When starting after a long layoff or advising others who are just starting I say stick to heavy compound lifts and keep it simple (stupid) K.I.S.S. Squat on Monday, bench and chins (weighted or assisted/static-hang/negatives depending on need) on say Tuesday or Wednesday, followed by deadlifts on Thursday or Friday. I might add a little cardio in the form of incline treadmill, brisk walking or easy jogging as a warm-up and on the in-between days and maybe shoulder press. I figure you start lower than you know you can do with the assumption that you will work your way up in small incremental steps.

For example I pick a goal such as two sets of 8 reps max on bench and start on 135 since I've been off for several years even though I'm sure I could push up 285+ pretty easily. If I hit my goal of two sets of 8 then I increase the weight the next week, this may be a little slow at first but I am keeping in mind that connective tissues and bones grow more slowly than muscle tissue. As long as I can hit say 5 reps per set on the next workout then it isn't too much, if I can do at least or more than two sets of whatever my goal is, 8 in this case (I may want higher reps on legs or less impact on shoulders or whatever), then I move up in whatever my most reasonable increment is the next week--5 or 10lbs.

Because you are already lean I'd focus on seeing small, regular incremental gains on those basics in the beginning and perhaps avoiding cardio. I assume you want to increase muscle mass of course. As long as your strength is either maintaining or increasing I am not overly concerned with weight staying the same or increasing slightly. If your strength in increasing you are seeing some sort of growth. Only when that growth plateaus would I look to adjusting macronutrients or focusing on isolation exercises of muscle groups.